André-Marie Tremblay - Academia.edu (original) (raw)
Papers by André-Marie Tremblay
Physical Review B, 1994
The observed magnetic spin susceptibility of high-temperature superconductors such as La 2−x Sr x... more The observed magnetic spin susceptibility of high-temperature superconductors such as La 2−x Sr x CuO 4 increases when x increases from zero, i.e. as one dopes away from half-filling. Recent Monte Carlo simulations of A. Moreo (Phys. Rev. B 48, 3380 (1993)) suggest that this behavior can be reproduced by the two-dimensional Hubbard model only at large coupling, namely, U/t of order 10. Using longer runs, our Monte Carlo simulations show that the same behavior as for U/t = 10 is obtained even in the intermediate coupling regime (U/t = 4), as long as the temperature is low enough (T = t/6) that strong antiferromagnetic correlations are building up at half-filling. These results are consistent with the fact that in two-dimensions, the GRPA should fail in the parameter range where it predicts a magnetic phase transition.
Physical Review A, 1985
A general formulation for the spectral noise S& of random linear resistor networks of arbitrary t... more A general formulation for the spectral noise S& of random linear resistor networks of arbitrary topology is given. General calculational methods based on Tellegen's theorem are illustrated for oneand two-probe configurations. For self-similar networks, we show the existence of a new exponent b, member of a whole new hierarchy of exponents characterizing the size dependence of the normalized noise spectrum W~-S~/8. b is shown to lie between the fractal dimension d and the resistance exponent-Pt.. b has been calculated for a large class of fractal structures: Sierpinski gaskets, X lattices, von Koch structures, etc. For percolating systems, W& is investigated for p &p, as well as for p &p,. In particular, an anomalous increase of the noise at p~p, is obtained. A finite-size-scaling function is proposed, and the corresponding exponent b is calculated in mean-field theory. I. INTRODUCTION. Statistical self-similarity is emerging as an important concept underlying the behavior of disordered systems. In percolation clusters, for example, the fractal dimension has been identified first; it was immediately realized, however, that this quantity and the correlation-length exponent did not suffice for a characterization of all the physical properties of these clusters. Alexander and Orbach and Rammal and Toulouse introduced the spectral dimension d to describe the spectrum of the Laplacian operator which appears in a large variety of linear physical problems. The geometrical property which most influences the spectral dimension is the number of closed loops of the fractal. It is an intrinsic geometrical property" independent of the embedding Euclidean space. Another such intrinsic property is the recently iptroduced ' spreading dimension d. Intuitively, it is plausible that an infinite number of exponents must be used to
Physical Review B, 1987
Analogies between critical phenomena and the continuous spectrum of scaling exponents associated ... more Analogies between critical phenomena and the continuous spectrum of scaling exponents associated with fractal measures are pointed out. The analogies are based first on the Hausdorff-Bernstein reconstruction theorem, which states that the positive integer moments suf5ce to characterize a probability distribution function with finite support, and second on the joint probability distribution for the positive integer moments. This joint probability distribution, which can be considered as a fixed point, is universal and exhibits both gap scaling and the infinite set of exponents. Monte Carlo simulations of the electrical properties of percolation clusters on the square and triangular lattices support this general result. Extensions to other fields where infinite sets of exponents have arisen, such as diAusion-limited aggregation and localization, should be straightforward.
Physical Review A, 1987
Each of the moments of the current distribution in self-similar networks scales with a different ... more Each of the moments of the current distribution in self-similar networks scales with a different exponent. The Legendre transform of these exponents as a function of the order of the moment is called f (a). In general f (a) has a fixed convexity, has a maximum value equal to the usual fractal dimension, is continuous, is positive, and has a finite support a;"&a&0, ". Also, it usually characterizes the asymptotic form of the current distribution. Here, explicit examples of physically acceptable exceptions to the behavior of f (a) are exhibited. In the first example, the moments near the zeroth one do not converge uniformly in the large-size limit, leading to an f (a) which has an apparent maximum at a finite value of a while the true maximum is at n,"=ao. In the second example, it is shown that f (ct) can take negative values in domains which are relevant for a full characterization of the current distribution. Disorder seems essential to obtain the latter behavior which for these systems compromises the interpretation of f (a) as a continuous set of fractal dimensions.
Physical Review B, 2014
The solution of a generalized impurity model lies at the heart of electronic structure calculatio... more The solution of a generalized impurity model lies at the heart of electronic structure calculations with dynamical mean-field theory (DMFT). In the strongly-correlated regime, the method of choice for solving the impurity model is the hybridization expansion continuous time quantum Monte Carlo (CT-HYB). Enhancements to the CT-HYB algorithm are critical for bringing new physical regimes within reach of current computational power. Taking advantage of the fact that the bottleneck in the algorithm is a product of hundreds of matrices, we present optimizations based on the introduction and combination of two concepts of more general applicability: a) skip lists and b) fast rejection of proposed configurations based on matrix bounds. Considering two very different test cases with d electrons, we find speedups of ∼ 25 up to ∼ 500 compared to the direct evaluation of the matrix product. Even larger speedups are likely with f electron systems and with clusters of correlated atoms.
Physical Review B, 1986
Raman and infrared spectra of linear-chain models of mixed crystals are investigated. Motion alon... more Raman and infrared spectra of linear-chain models of mixed crystals are investigated. Motion along more than one direction is allowed. Much of the phenomenology of real linear-chain compounds such as ZrS3 "Se can be qualitatively accounted for: preservation of the Raman and infrared symmetries present in the parent pure compounds, one-, two-, and three-mode behavior, disorder-induced line~idths, and line-shape asymmetries. The physical nature and significance of many of these observed phenomena is clarified. I. INTRODUCTION The type of quenched-in disorder present in various condensed systems can sometimes be classified in various categories. Disorder in the positions of the atoms influences the elastic x-ray scattering spectrmn for example. This positional disorder coexists with topological order when the disordered lattice can be mapped into an ordered lattice without breaking bonds. Mass and force-constant disorder, on the other hand, have only limited influence on the elastic x-ray spectrum (they enter indirectly in the structure factor), but they manifest themselves drastically in the dynamic properties probed by neutron or light scattering. These spectroscopies are also influenced by the disorder in the effective light-matter coupling constants. The latter disorder (e.g. , polarizability for Raman scattering) is clearly not unrelatel to the disorder in mass, force constant, or position, but the relation can be quite complicated. Predicting the detailed light scattering spectrum of a general disordered system, while possible in principle, is an extremely compHcated task. Nevertheless, one would like to be able to extract some information on any given disordered system from its light scattering spectrum. Qu»mtative results can also be extremely useful. For example, it is generally believed that the Raman spectrutn of amorphous semiconductors such as' Ge or Si reflects the total density of states of these systems because the momentum conservation rule is broken so that more or less all modes become Raman active. While certainly not rigorously valid, this observation may be extremely useful in practice. Mixed crystals represent a class of systems which in some sense are inteii~ediate between the amorphous solids and the pure crystals. These crystals have only substitutional disorder, i.e. , atoms of one kind or another go at random into the sites of an ordered lattice. They thus have relatively little disorder: Their elastic x-ray spectrum looks like that of a pure crystal. They have certainly no topological disorder and the position disorder, if present, is very small. Their light scattering spectrum is
Physical Review B, 1993
It is shown that the Hubbard model in the intermediate-coupling regime can qualitatively explain ... more It is shown that the Hubbard model in the intermediate-coupling regime can qualitatively explain neutron-scattering experiments in La2 "Sr"Cu04 only if there are strong magnetic fluctuations in the system. By contrast, the marginal-Fermi-liquid approach explains the data without appealing at all to strong magnetic fluctuations. It is shown that the strength of the magnetic fluctuations can be estimated by detecting incommensurate peaks located near the zone center using neutron-scattering experiments. The magnetic structure factor appears as an ideal quantity to make quantitative comparisons between theory and experiment in high-temperature superconductors. Indeed, this quantity can both be computed reliably and measured in detail as a function of wave vector and frequency. On the experimental side, there have been several detailed neutron-scattering measurements of this quantity in the new superconductors. '
Physical Review B, 1981
This paper is addressed to a theoretical understanding of the relation proposed by Voss and Clark... more This paper is addressed to a theoretical understanding of the relation proposed by Voss and Clarke between nonequilibrium steady-state voltage fluctuations and equilibrium fluctuations in the band-limited Johnson-noise power. A nonlinear Langevin model is presented which satisfies local charge conservation and the fluctuation-dissipation theorem, and exhibits Gaussian equaltime statistics. The mode couplings in this model yield, in the appropriate limit, a non-Gaussian component in the equilibrium four-time voltage correlation function. This component can be interpreted in terms of equilibrium resistance fluctuations. It is also shown that the same mode-coupling terms give a small fluctuation renormalization of the average resistance. Our model is related to recently proposed Fokker-Planck models, in which local transport coefficients are functions of the instantaneous values of the state variables.
Physical Review B, 1992
The resistance noise of random conductor-insulator mixtures is studied in the case where the insu... more The resistance noise of random conductor-insulator mixtures is studied in the case where the insulators have a small but finite conductance. The conductance noise of superconductor-conductor mixtures is similarly studied when the superconductors have a small but finite resistance. The Migdal-Kadanoff renormalization-group calculations that lead to the appropriate linear and nonlinear scaling fields for these problems are discussed in detail. The corresponding homogeneity relations for the total noise are valid near the unstable percolation fixed point whatever the relative size of the microscopic noises. The exponents of the superconductor-conductor mixture appear naturally in the scaling form of the noise coming from the imperfect insulators. Analogously, the exponents of the conductor-insulator mixture enter in the scaling form of the noise coming from the imperfect superconductors in the superconductor-conductor problem. Monte Carlo simulations in two and three dimensions confirm that the scaling predictions are valid well beyond the domain of applicability of the Migdal-Kadanoff approach. For all multifractal moments and both types of mixtures, there is a single crossover exponent and a single correlation length associated with the ratio of the microscopic conductances.
Physical Review B, 1992
In the trichalcogenide family of compounds Zr& "Hf"S3 there is a frequency range where the optic ... more In the trichalcogenide family of compounds Zr& "Hf"S3 there is a frequency range where the optic modes are expected to be describable by a simple one-dimensional model. It is shown that the disorderinduced linewidth in the relevant frequency range could be consistent with theoretical calculations for a simple diatomic chain model. The vibrations involved are along the chain direction and are of Bg type. All the Bg modes of this family of compounds are also here unequivocally identified.
Physics Letters A, 1980
Using an extension of the Langevin method, we calculate the fluctuations of a fluid about a stati... more Using an extension of the Langevin method, we calculate the fluctuations of a fluid about a stationary state held away from global thermal equilibrium by a temperature gradient or shear flow. In the former case, the Brillouin peaks in the light scattering spectrum acquire an asymmetry that is qualitatively similar to earlier results but different in detail.
Physical Review Letters, 1985
New results for the magnitude of flicker noise, considered as resistance fluctuations, in random ... more New results for the magnitude of flicker noise, considered as resistance fluctuations, in random resistor networks are reported. Near the percolation threshold p" the magnitude of the relative noise is shown to diverge as (pp,) ". The new exponent K is calculated by various methods: Monte Carlo simulations, effective-medium theory, and position-space renormalization group. Exponents pertaining to higher-order cumulants of the resistance fluctuations are also calculated. The possible implications of our results for ongoing experiments on metal-insulator mixtures and cermets are also discussed.
Physical Review Letters, 1990
A new program of characterization of multifractal moments is proposed. For the circle map, the us... more A new program of characterization of multifractal moments is proposed. For the circle map, the usual multifractal moments are described by both scaling exponents and amplitudes. These amplitudes depend sensitively on the starting point of the time series used to define these moments. This leads naturally to a statistical description which is universal and analogous to that used in critical phenomena and in other fields where multifractals occur. This description can be used not only at the critical point, but also in the crossover region where the analog of the correlation length is large but not infinite.
Physical Review Letters, 1987
Cohn s theorem is extended to the case of circuit elements with the nonlinear I-V characteristic ... more Cohn s theorem is extended to the case of circuit elements with the nonlinear I-V characteristic V rI'. This simplifies the study of resistance noise in nonlinear resistor networks. Exact exponent inequalities are derived. Fractal and percolating structures are considered. The infinite number of exponents necessary to characterize completely the electrical properties of linear and nonlinear percolating networks are calculated within the Migdal-Kadanoff approximation.
Physical Review Letters, 2006
Physical Review B, 2007
We study the properties of t − t ′ − V model of hard-core bosons on the triangular lattice that c... more We study the properties of t − t ′ − V model of hard-core bosons on the triangular lattice that can be realized in optical lattices. By mapping to the spin-1/2 XXZ model in a field, we determine the phase diagram of the t − V model where the supersolid characterized by the ordering pattern (x, x, −2x ′) ("ferrimagnetic" or SS A) is a ground state for chemical potential µ > 3V. By turning on either temperature or t ′ at half-filling (µ = 3V), we find a first order transition from SS A to the elusive supersolid characterized by the (x, −x, 0) ordering pattern ("antiferromagnetic" or SS C). In addition, we find a large region where a superfluid phase becomes a solid upon raising temperature at fixed chemical potential. This is an analog of the Pomeranchuk effect driven by the large entropic effects associated with geometric frustration on the triangular lattice.
Physical Review B, 2004
Three well-known perturbative approaches to deriving low-energy effective theories, the degenerat... more Three well-known perturbative approaches to deriving low-energy effective theories, the degenerate Brillouin-Wigner perturbation theory (projection method), the canonical transformation, and the resolvent methods are compared. We use the Hubbard model as an example to show how, to fourth order in hopping t, all methods lead to the same effective theory, namely the t-J model with ring exchange and various correlated hoppings. We emphasize subtle technical difficulties that make such a derivation less trivial to carry out for orders higher than second. We also show that in higher orders, different approaches can lead to seemingly different forms for the low-energy Hamiltonian. All of these forms are equivalent since they are connected by an additional unitary transformation whose generator is given explicitly. The importance of transforming the operators is emphasized and the equivalence of their transformed structure within the different approaches is also demonstrated.
Physical Review B, 2009
Discontinuities in elastic constants are detected at the superconducting transition of layered or... more Discontinuities in elastic constants are detected at the superconducting transition of layered organic conductors κ-(BEDT-TTF)2X by longitudinal and transverse ultrasonic velocity measurements. Symmetry arguments show that discontinuities in shear elastic constants can be explained in the orthorhombic compound only if the superconducting order parameter has a mixed character that can be of two types, either A1g + B1g or B2g + B3g in the classification of irreducible representations of the orthorhombic point group D 2h. Consistency with other measurements suggests that the A1g + B1g (dxy + d z(x+y)) possibility is realized. Such clear symmetry-imposed signatures of mixed order parameters have not been observed in other superconducting compounds.
Physical Review B, 1994
The observed magnetic spin susceptibility of high-temperature superconductors such as La 2−x Sr x... more The observed magnetic spin susceptibility of high-temperature superconductors such as La 2−x Sr x CuO 4 increases when x increases from zero, i.e. as one dopes away from half-filling. Recent Monte Carlo simulations of A. Moreo (Phys. Rev. B 48, 3380 (1993)) suggest that this behavior can be reproduced by the two-dimensional Hubbard model only at large coupling, namely, U/t of order 10. Using longer runs, our Monte Carlo simulations show that the same behavior as for U/t = 10 is obtained even in the intermediate coupling regime (U/t = 4), as long as the temperature is low enough (T = t/6) that strong antiferromagnetic correlations are building up at half-filling. These results are consistent with the fact that in two-dimensions, the GRPA should fail in the parameter range where it predicts a magnetic phase transition.
Physical Review A, 1985
A general formulation for the spectral noise S& of random linear resistor networks of arbitrary t... more A general formulation for the spectral noise S& of random linear resistor networks of arbitrary topology is given. General calculational methods based on Tellegen's theorem are illustrated for oneand two-probe configurations. For self-similar networks, we show the existence of a new exponent b, member of a whole new hierarchy of exponents characterizing the size dependence of the normalized noise spectrum W~-S~/8. b is shown to lie between the fractal dimension d and the resistance exponent-Pt.. b has been calculated for a large class of fractal structures: Sierpinski gaskets, X lattices, von Koch structures, etc. For percolating systems, W& is investigated for p &p, as well as for p &p,. In particular, an anomalous increase of the noise at p~p, is obtained. A finite-size-scaling function is proposed, and the corresponding exponent b is calculated in mean-field theory. I. INTRODUCTION. Statistical self-similarity is emerging as an important concept underlying the behavior of disordered systems. In percolation clusters, for example, the fractal dimension has been identified first; it was immediately realized, however, that this quantity and the correlation-length exponent did not suffice for a characterization of all the physical properties of these clusters. Alexander and Orbach and Rammal and Toulouse introduced the spectral dimension d to describe the spectrum of the Laplacian operator which appears in a large variety of linear physical problems. The geometrical property which most influences the spectral dimension is the number of closed loops of the fractal. It is an intrinsic geometrical property" independent of the embedding Euclidean space. Another such intrinsic property is the recently iptroduced ' spreading dimension d. Intuitively, it is plausible that an infinite number of exponents must be used to
Physical Review B, 1987
Analogies between critical phenomena and the continuous spectrum of scaling exponents associated ... more Analogies between critical phenomena and the continuous spectrum of scaling exponents associated with fractal measures are pointed out. The analogies are based first on the Hausdorff-Bernstein reconstruction theorem, which states that the positive integer moments suf5ce to characterize a probability distribution function with finite support, and second on the joint probability distribution for the positive integer moments. This joint probability distribution, which can be considered as a fixed point, is universal and exhibits both gap scaling and the infinite set of exponents. Monte Carlo simulations of the electrical properties of percolation clusters on the square and triangular lattices support this general result. Extensions to other fields where infinite sets of exponents have arisen, such as diAusion-limited aggregation and localization, should be straightforward.
Physical Review A, 1987
Each of the moments of the current distribution in self-similar networks scales with a different ... more Each of the moments of the current distribution in self-similar networks scales with a different exponent. The Legendre transform of these exponents as a function of the order of the moment is called f (a). In general f (a) has a fixed convexity, has a maximum value equal to the usual fractal dimension, is continuous, is positive, and has a finite support a;"&a&0, ". Also, it usually characterizes the asymptotic form of the current distribution. Here, explicit examples of physically acceptable exceptions to the behavior of f (a) are exhibited. In the first example, the moments near the zeroth one do not converge uniformly in the large-size limit, leading to an f (a) which has an apparent maximum at a finite value of a while the true maximum is at n,"=ao. In the second example, it is shown that f (ct) can take negative values in domains which are relevant for a full characterization of the current distribution. Disorder seems essential to obtain the latter behavior which for these systems compromises the interpretation of f (a) as a continuous set of fractal dimensions.
Physical Review B, 2014
The solution of a generalized impurity model lies at the heart of electronic structure calculatio... more The solution of a generalized impurity model lies at the heart of electronic structure calculations with dynamical mean-field theory (DMFT). In the strongly-correlated regime, the method of choice for solving the impurity model is the hybridization expansion continuous time quantum Monte Carlo (CT-HYB). Enhancements to the CT-HYB algorithm are critical for bringing new physical regimes within reach of current computational power. Taking advantage of the fact that the bottleneck in the algorithm is a product of hundreds of matrices, we present optimizations based on the introduction and combination of two concepts of more general applicability: a) skip lists and b) fast rejection of proposed configurations based on matrix bounds. Considering two very different test cases with d electrons, we find speedups of ∼ 25 up to ∼ 500 compared to the direct evaluation of the matrix product. Even larger speedups are likely with f electron systems and with clusters of correlated atoms.
Physical Review B, 1986
Raman and infrared spectra of linear-chain models of mixed crystals are investigated. Motion alon... more Raman and infrared spectra of linear-chain models of mixed crystals are investigated. Motion along more than one direction is allowed. Much of the phenomenology of real linear-chain compounds such as ZrS3 "Se can be qualitatively accounted for: preservation of the Raman and infrared symmetries present in the parent pure compounds, one-, two-, and three-mode behavior, disorder-induced line~idths, and line-shape asymmetries. The physical nature and significance of many of these observed phenomena is clarified. I. INTRODUCTION The type of quenched-in disorder present in various condensed systems can sometimes be classified in various categories. Disorder in the positions of the atoms influences the elastic x-ray scattering spectrmn for example. This positional disorder coexists with topological order when the disordered lattice can be mapped into an ordered lattice without breaking bonds. Mass and force-constant disorder, on the other hand, have only limited influence on the elastic x-ray spectrum (they enter indirectly in the structure factor), but they manifest themselves drastically in the dynamic properties probed by neutron or light scattering. These spectroscopies are also influenced by the disorder in the effective light-matter coupling constants. The latter disorder (e.g. , polarizability for Raman scattering) is clearly not unrelatel to the disorder in mass, force constant, or position, but the relation can be quite complicated. Predicting the detailed light scattering spectrum of a general disordered system, while possible in principle, is an extremely compHcated task. Nevertheless, one would like to be able to extract some information on any given disordered system from its light scattering spectrum. Qu»mtative results can also be extremely useful. For example, it is generally believed that the Raman spectrutn of amorphous semiconductors such as' Ge or Si reflects the total density of states of these systems because the momentum conservation rule is broken so that more or less all modes become Raman active. While certainly not rigorously valid, this observation may be extremely useful in practice. Mixed crystals represent a class of systems which in some sense are inteii~ediate between the amorphous solids and the pure crystals. These crystals have only substitutional disorder, i.e. , atoms of one kind or another go at random into the sites of an ordered lattice. They thus have relatively little disorder: Their elastic x-ray spectrum looks like that of a pure crystal. They have certainly no topological disorder and the position disorder, if present, is very small. Their light scattering spectrum is
Physical Review B, 1993
It is shown that the Hubbard model in the intermediate-coupling regime can qualitatively explain ... more It is shown that the Hubbard model in the intermediate-coupling regime can qualitatively explain neutron-scattering experiments in La2 "Sr"Cu04 only if there are strong magnetic fluctuations in the system. By contrast, the marginal-Fermi-liquid approach explains the data without appealing at all to strong magnetic fluctuations. It is shown that the strength of the magnetic fluctuations can be estimated by detecting incommensurate peaks located near the zone center using neutron-scattering experiments. The magnetic structure factor appears as an ideal quantity to make quantitative comparisons between theory and experiment in high-temperature superconductors. Indeed, this quantity can both be computed reliably and measured in detail as a function of wave vector and frequency. On the experimental side, there have been several detailed neutron-scattering measurements of this quantity in the new superconductors. '
Physical Review B, 1981
This paper is addressed to a theoretical understanding of the relation proposed by Voss and Clark... more This paper is addressed to a theoretical understanding of the relation proposed by Voss and Clarke between nonequilibrium steady-state voltage fluctuations and equilibrium fluctuations in the band-limited Johnson-noise power. A nonlinear Langevin model is presented which satisfies local charge conservation and the fluctuation-dissipation theorem, and exhibits Gaussian equaltime statistics. The mode couplings in this model yield, in the appropriate limit, a non-Gaussian component in the equilibrium four-time voltage correlation function. This component can be interpreted in terms of equilibrium resistance fluctuations. It is also shown that the same mode-coupling terms give a small fluctuation renormalization of the average resistance. Our model is related to recently proposed Fokker-Planck models, in which local transport coefficients are functions of the instantaneous values of the state variables.
Physical Review B, 1992
The resistance noise of random conductor-insulator mixtures is studied in the case where the insu... more The resistance noise of random conductor-insulator mixtures is studied in the case where the insulators have a small but finite conductance. The conductance noise of superconductor-conductor mixtures is similarly studied when the superconductors have a small but finite resistance. The Migdal-Kadanoff renormalization-group calculations that lead to the appropriate linear and nonlinear scaling fields for these problems are discussed in detail. The corresponding homogeneity relations for the total noise are valid near the unstable percolation fixed point whatever the relative size of the microscopic noises. The exponents of the superconductor-conductor mixture appear naturally in the scaling form of the noise coming from the imperfect insulators. Analogously, the exponents of the conductor-insulator mixture enter in the scaling form of the noise coming from the imperfect superconductors in the superconductor-conductor problem. Monte Carlo simulations in two and three dimensions confirm that the scaling predictions are valid well beyond the domain of applicability of the Migdal-Kadanoff approach. For all multifractal moments and both types of mixtures, there is a single crossover exponent and a single correlation length associated with the ratio of the microscopic conductances.
Physical Review B, 1992
In the trichalcogenide family of compounds Zr& "Hf"S3 there is a frequency range where the optic ... more In the trichalcogenide family of compounds Zr& "Hf"S3 there is a frequency range where the optic modes are expected to be describable by a simple one-dimensional model. It is shown that the disorderinduced linewidth in the relevant frequency range could be consistent with theoretical calculations for a simple diatomic chain model. The vibrations involved are along the chain direction and are of Bg type. All the Bg modes of this family of compounds are also here unequivocally identified.
Physics Letters A, 1980
Using an extension of the Langevin method, we calculate the fluctuations of a fluid about a stati... more Using an extension of the Langevin method, we calculate the fluctuations of a fluid about a stationary state held away from global thermal equilibrium by a temperature gradient or shear flow. In the former case, the Brillouin peaks in the light scattering spectrum acquire an asymmetry that is qualitatively similar to earlier results but different in detail.
Physical Review Letters, 1985
New results for the magnitude of flicker noise, considered as resistance fluctuations, in random ... more New results for the magnitude of flicker noise, considered as resistance fluctuations, in random resistor networks are reported. Near the percolation threshold p" the magnitude of the relative noise is shown to diverge as (pp,) ". The new exponent K is calculated by various methods: Monte Carlo simulations, effective-medium theory, and position-space renormalization group. Exponents pertaining to higher-order cumulants of the resistance fluctuations are also calculated. The possible implications of our results for ongoing experiments on metal-insulator mixtures and cermets are also discussed.
Physical Review Letters, 1990
A new program of characterization of multifractal moments is proposed. For the circle map, the us... more A new program of characterization of multifractal moments is proposed. For the circle map, the usual multifractal moments are described by both scaling exponents and amplitudes. These amplitudes depend sensitively on the starting point of the time series used to define these moments. This leads naturally to a statistical description which is universal and analogous to that used in critical phenomena and in other fields where multifractals occur. This description can be used not only at the critical point, but also in the crossover region where the analog of the correlation length is large but not infinite.
Physical Review Letters, 1987
Cohn s theorem is extended to the case of circuit elements with the nonlinear I-V characteristic ... more Cohn s theorem is extended to the case of circuit elements with the nonlinear I-V characteristic V rI'. This simplifies the study of resistance noise in nonlinear resistor networks. Exact exponent inequalities are derived. Fractal and percolating structures are considered. The infinite number of exponents necessary to characterize completely the electrical properties of linear and nonlinear percolating networks are calculated within the Migdal-Kadanoff approximation.
Physical Review Letters, 2006
Physical Review B, 2007
We study the properties of t − t ′ − V model of hard-core bosons on the triangular lattice that c... more We study the properties of t − t ′ − V model of hard-core bosons on the triangular lattice that can be realized in optical lattices. By mapping to the spin-1/2 XXZ model in a field, we determine the phase diagram of the t − V model where the supersolid characterized by the ordering pattern (x, x, −2x ′) ("ferrimagnetic" or SS A) is a ground state for chemical potential µ > 3V. By turning on either temperature or t ′ at half-filling (µ = 3V), we find a first order transition from SS A to the elusive supersolid characterized by the (x, −x, 0) ordering pattern ("antiferromagnetic" or SS C). In addition, we find a large region where a superfluid phase becomes a solid upon raising temperature at fixed chemical potential. This is an analog of the Pomeranchuk effect driven by the large entropic effects associated with geometric frustration on the triangular lattice.
Physical Review B, 2004
Three well-known perturbative approaches to deriving low-energy effective theories, the degenerat... more Three well-known perturbative approaches to deriving low-energy effective theories, the degenerate Brillouin-Wigner perturbation theory (projection method), the canonical transformation, and the resolvent methods are compared. We use the Hubbard model as an example to show how, to fourth order in hopping t, all methods lead to the same effective theory, namely the t-J model with ring exchange and various correlated hoppings. We emphasize subtle technical difficulties that make such a derivation less trivial to carry out for orders higher than second. We also show that in higher orders, different approaches can lead to seemingly different forms for the low-energy Hamiltonian. All of these forms are equivalent since they are connected by an additional unitary transformation whose generator is given explicitly. The importance of transforming the operators is emphasized and the equivalence of their transformed structure within the different approaches is also demonstrated.
Physical Review B, 2009
Discontinuities in elastic constants are detected at the superconducting transition of layered or... more Discontinuities in elastic constants are detected at the superconducting transition of layered organic conductors κ-(BEDT-TTF)2X by longitudinal and transverse ultrasonic velocity measurements. Symmetry arguments show that discontinuities in shear elastic constants can be explained in the orthorhombic compound only if the superconducting order parameter has a mixed character that can be of two types, either A1g + B1g or B2g + B3g in the classification of irreducible representations of the orthorhombic point group D 2h. Consistency with other measurements suggests that the A1g + B1g (dxy + d z(x+y)) possibility is realized. Such clear symmetry-imposed signatures of mixed order parameters have not been observed in other superconducting compounds.