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Papers by Katarina Uzelac

Springer eBooks, 1980

In contrast with classical systems, quantum systems exhibit fluctuations already at T = 0 due to ... more In contrast with classical systems, quantum systems exhibit fluctuations already at T = 0 due to the nature of quantum mechanics. A wide range of quantum systems show interesting transitions at T = 0 by varying a given parameter. This should be compared with the transitions in temperature of classical systems and, in many cases, a rigorous mapping has been established. The equivalent of a T = 0 quantum system in D dimension is generally a D+1 classical system. This comes from the fact that a quantum hamiltonian contains its own dynamics and thus the time plays the role of an extra dimentionality So, an interesting first step to understand the physics of quantum systems is to study their ground state properties. This is either an interesting problem in itself or an indirect way to study the classical equivalent.

Springer series in synergetics, 1981

A real-space renormalization-group method well suited for studying phase transitions at T = 0 in ... more A real-space renormalization-group method well suited for studying phase transitions at T = 0 in quantum systems is presented and applied to a generalized spin 1/2 planar hamiltonian on the triangular lattice, which includes ferromagnetic and anti-ferromagnetic XY models as limiting cases. This provides a description of the effects of frustration in quantum systems.

Journal of Applied Physics, 1979

A T=0 real-space renormalization-group method is presented and applied to the quantum 1D transver... more A T=0 real-space renormalization-group method is presented and applied to the quantum 1D transverse field Ising model in the presence of a longitudinal field. This is an indirect way to study the equation of state of the equivalent 2D classical Ising model at finite temperature. When the longitudinal field is purely imaginary we obtain a new critical behavior which is

Physical Review Letters, Jun 9, 1980

PHYSICAL REVIEW LETTERS 9 JUNE 1980 results. Finally, with an increase in temperature, we observe... more PHYSICAL REVIEW LETTERS 9 JUNE 1980 results. Finally, with an increase in temperature, we observe an overall broadening and gradual decrease in the intensity of the spin-wave peaks. No qualitative change in the spectra was observed on cooling the sample through T"at 23 K. In summary, we have established a band of spinwave excitations in 1D Ising-type antiferromagnetic system. These excitations seem to be related to the motion of domain-wall pairs in the chain. The motion of domain walls should also be manifested in the central component of the S"(Q, u) response function. It was first predicted by Villain" that at low temperatures the spin dynamics of an antiferromagnetic linear chain can be governed by propagation of thermally excited domain walls. Such a problem is presently under investigation. We gratefully acknowledge useful discussions with G. F. Reiter, N. Ishimura, and H. Shiba. We are thankful to the authors of Ref. 7 for communicating their results prior to publication. This research was supported by the Division of Basic Energy Sciences, U. S. Department of Energy, under Contract No. DE-AC02-7cCH00016.

Springer eBooks, 1981

Quite a long time ago Yang and Lee [1] pointed out the importance of the relationship between the... more Quite a long time ago Yang and Lee [1] pointed out the importance of the relationship between the zeros of the partition function and the singularities of thermodynamic quantities occuring in a second order phase transition. They also proved the theorem that for the ferromagnetic Ising model these zeros lie on the unit circle in the complex activity plane z = exp(-2h/kT) where h is a complex symmetry breaking field and T is the temperature. In the thermodynamic limit they are distributed by some density g(h). Above TC this distribution has a gap around the real axis, which closes when approaching TC. Since g(h) is proportional to the spontaneous magnetization, the edges of this gap are branching points for the magnetization.

We present numerical investigations of the short-time dynamics at criticality in the 1D Potts mod... more We present numerical investigations of the short-time dynamics at criticality in the 1D Potts model with power-law decaying interactions of the form 1/r 1+σ. The scaling properties of the magnetization, autocorrelation function and time correlations of the magnetization are studied. The dynamical critical exponents θ ′ and z are derived in the cases q = 2 and q = 3 for several values of the parameter σ belonging to the nontrivial critical regime.

Phase transitions inside the pores of an aerogel are investigated by modelizing the aerogel struc... more Phase transitions inside the pores of an aerogel are investigated by modelizing the aerogel structure by diffusion-limited cluster-cluster aggregation on a cubic lattice in a finite box and considering q-states Potts variables on the empty sites interacting via nearest-neighbours. Using a finite size scaling analysing of Monte-Carlo numerical results, it is concluded that for q=4 the transition changes from first order to second order as the aerogel concentration (density) increases. Comparison is made with the case q=3 (where the first order transition is weaker in three dimensions) and with the case q=4 but for randomly (non correlated) occupied sites. Possible applications to experiments are discussed.

Phase transitions inside the pores of an aerogel are investigated by modelizing the aerogel struc... more Phase transitions inside the pores of an aerogel are investigated by modelizing the aerogel structure by diffusion-limited cluster-cluster aggregation on a cubic lattice in a finite box and considering q-states Potts variables on the empty sites interacting via nearest-neighbours. Using a finite size scaling analysing of Monte-Carlo numerical results, it is concluded that for q = 4 the transition changes from first order to second order as the aerogel concentration (density) increases. Comparison is made with the case q = 3 (where the first order transition is weaker in three dimensions) and with the case q = 4 but for randomly (non correlated) occupied sites. Possible applications to experiments are discussed.

Physical Review Letters, 1995

ABSTRACT An aerogel of volume fraction c is modeled on a 3D lattice using diffusion-limited clust... more ABSTRACT An aerogel of volume fraction c is modeled on a 3D lattice using diffusion-limited cluster-cluster aggregation in cubic boxes of sizes up to 20×20×20. A set of q-state Potts variables are disposed on the nonoccupied sites and their order-disorder phase transition is studied by means of a Monte Carlo technique for q = 3 and q = 4. It is found that the transition changes from first to second order above a nonzero threshold value of c. A comparison is made with the case of randomly occupied sites. The possible application to recent experimental results is discussed.

The first-order phase transition in the one-dimensional q-state Potts model with long-range inter... more The first-order phase transition in the one-dimensional q-state Potts model with long-range interactions decaying with distance as 1 r 1 ¡ σ, has been studied by Monte Carlo numerical simulations for 0 ¢ σ £ 1 and integer values of q ¤ 2. On the basis of the finite-size scaling analysis of interface free energy ΔFL, specific heat and Binder’s fourth order cumulant, we obtain the first-order transition which occurs for σ below a threshold value σc ¥ q ¦. The subject of our study is the one-dimensional (1d) Potts model with ferromagnetic long-range (LR) interactions decaying with distance as 1 r 1 ¡ σ, defined by the Hamiltonian H §© ¨ ∑ i � j J � i ¨ j � 1 ¡ σ δ ¥ si � s j ¦ � (1) where J ¤ 0, si denotes the q-state Potts variable at site i, δ is the Kronecker symbol, and summation is taken over all pairs in the system. The phase transition at nonzero temperature, shown rigorously [1] for the Ising ¥ q § 2 ¦ case with σ £ 1 and by renormalization group for the continuous n-compon...

We examine the order of the phase transition in the Potts model by using the graph representation... more We examine the order of the phase transition in the Potts model by using the graph representation for the partition function, which allows treating a non-integer number of Potts states. The order of transition is determined by the analysis of the shape of the graph-weight probability distribution. The approach is illustrated on special cases of the one-dimensional Potts model with long-range interactions and on its mean-ÿeld limit.

We present the numerical study of the one-dimensional Potts model with power-law decaying ferroma... more We present the numerical study of the one-dimensional Potts model with power-law decaying ferromagnetic interactions. The largest cluster probability distribution is obtained by Monte Carlo simulations using the Swendsen-Wang cluster algorithm with cumulative probabilities. The ÿnite-size scaling analysis of the largest cluster is used to derive the critical behaviour in the non-classical regime of this model for various values of q. The models involving long-range interactions have an important role in describing many complex systems, from physics to economy or biology, but the equilibrium critical phenomena in these models are still not well understood and deserve further attention. We consider here the 1d Potts model with long-range interactions deÿned by the Hamiltonian

The effect of the quenched random dilution on the ferromagnetic transitions, in particular, the c... more The effect of the quenched random dilution on the ferromagnetic transitions, in particular, the conversion from the first-to second-order transition is discussed. The new results are presented for the diluted three-dimensional three-state Potts model. The critical exponents of the disorder-induced second-order phase transition are derived by the finite-size scaling analysis of the moments of the energy and the largest cluster, obtained from the Monte Carlo simulations.

We have performed exact analytical calculations of the cluster probability distribution and inter... more We have performed exact analytical calculations of the cluster probability distribution and interface free energy in the finite q-state Potts chains with interactions decaying with distance r as r^(1+sigma). By presenting the partition function in form of the polynomial in q, the advantage of using the Hamiltonian configurations compared with graph or connectivity approach was examined. Scaling analysis of the probability performed for large q (q >= 16) yields the first-order phase transition for 0 < sigma < 1.

The invaded cluster algorithm [1] is generalized [2] to the tricritical point on the example of 2... more The invaded cluster algorithm [1] is generalized [2] to the tricritical point on the example of 2d Potts model with annealed dilution. Self-regulating procedure that locates the tricritical point in the two-parameter space spanned by temperature and chemical potential of vacancies is constructed based on geometrical arguments. The tricritical point is identified as a simultaneous percolation of the Fortuin-Kastelyn cluster and the geometrical cluster consisting of vacancies and isolated spins. The tricritical values of parameters and concentration are presented for q=1, 2, 3 and found to be in a good agreement with the best known results [3]. Scaling properties of the percolating scaling cluster and related critical exponents are also derived. Based on the idea that effective correlation of vacancies is important at the tricritical point, we also examine alternative stopping rules within generalized IC algorithm, and possible extension to higher dimensions. [1] J. Machta, Y. S. Choi...

Springer eBooks, 1980

In contrast with classical systems, quantum systems exhibit fluctuations already at T = 0 due to ... more In contrast with classical systems, quantum systems exhibit fluctuations already at T = 0 due to the nature of quantum mechanics. A wide range of quantum systems show interesting transitions at T = 0 by varying a given parameter. This should be compared with the transitions in temperature of classical systems and, in many cases, a rigorous mapping has been established. The equivalent of a T = 0 quantum system in D dimension is generally a D+1 classical system. This comes from the fact that a quantum hamiltonian contains its own dynamics and thus the time plays the role of an extra dimentionality So, an interesting first step to understand the physics of quantum systems is to study their ground state properties. This is either an interesting problem in itself or an indirect way to study the classical equivalent.

Springer series in synergetics, 1981

A real-space renormalization-group method well suited for studying phase transitions at T = 0 in ... more A real-space renormalization-group method well suited for studying phase transitions at T = 0 in quantum systems is presented and applied to a generalized spin 1/2 planar hamiltonian on the triangular lattice, which includes ferromagnetic and anti-ferromagnetic XY models as limiting cases. This provides a description of the effects of frustration in quantum systems.

Journal of Applied Physics, 1979

A T=0 real-space renormalization-group method is presented and applied to the quantum 1D transver... more A T=0 real-space renormalization-group method is presented and applied to the quantum 1D transverse field Ising model in the presence of a longitudinal field. This is an indirect way to study the equation of state of the equivalent 2D classical Ising model at finite temperature. When the longitudinal field is purely imaginary we obtain a new critical behavior which is

Physical Review Letters, Jun 9, 1980

PHYSICAL REVIEW LETTERS 9 JUNE 1980 results. Finally, with an increase in temperature, we observe... more PHYSICAL REVIEW LETTERS 9 JUNE 1980 results. Finally, with an increase in temperature, we observe an overall broadening and gradual decrease in the intensity of the spin-wave peaks. No qualitative change in the spectra was observed on cooling the sample through T"at 23 K. In summary, we have established a band of spinwave excitations in 1D Ising-type antiferromagnetic system. These excitations seem to be related to the motion of domain-wall pairs in the chain. The motion of domain walls should also be manifested in the central component of the S"(Q, u) response function. It was first predicted by Villain" that at low temperatures the spin dynamics of an antiferromagnetic linear chain can be governed by propagation of thermally excited domain walls. Such a problem is presently under investigation. We gratefully acknowledge useful discussions with G. F. Reiter, N. Ishimura, and H. Shiba. We are thankful to the authors of Ref. 7 for communicating their results prior to publication. This research was supported by the Division of Basic Energy Sciences, U. S. Department of Energy, under Contract No. DE-AC02-7cCH00016.

Springer eBooks, 1981

Quite a long time ago Yang and Lee [1] pointed out the importance of the relationship between the... more Quite a long time ago Yang and Lee [1] pointed out the importance of the relationship between the zeros of the partition function and the singularities of thermodynamic quantities occuring in a second order phase transition. They also proved the theorem that for the ferromagnetic Ising model these zeros lie on the unit circle in the complex activity plane z = exp(-2h/kT) where h is a complex symmetry breaking field and T is the temperature. In the thermodynamic limit they are distributed by some density g(h). Above TC this distribution has a gap around the real axis, which closes when approaching TC. Since g(h) is proportional to the spontaneous magnetization, the edges of this gap are branching points for the magnetization.

We present numerical investigations of the short-time dynamics at criticality in the 1D Potts mod... more We present numerical investigations of the short-time dynamics at criticality in the 1D Potts model with power-law decaying interactions of the form 1/r 1+σ. The scaling properties of the magnetization, autocorrelation function and time correlations of the magnetization are studied. The dynamical critical exponents θ ′ and z are derived in the cases q = 2 and q = 3 for several values of the parameter σ belonging to the nontrivial critical regime.

Phase transitions inside the pores of an aerogel are investigated by modelizing the aerogel struc... more Phase transitions inside the pores of an aerogel are investigated by modelizing the aerogel structure by diffusion-limited cluster-cluster aggregation on a cubic lattice in a finite box and considering q-states Potts variables on the empty sites interacting via nearest-neighbours. Using a finite size scaling analysing of Monte-Carlo numerical results, it is concluded that for q=4 the transition changes from first order to second order as the aerogel concentration (density) increases. Comparison is made with the case q=3 (where the first order transition is weaker in three dimensions) and with the case q=4 but for randomly (non correlated) occupied sites. Possible applications to experiments are discussed.

Phase transitions inside the pores of an aerogel are investigated by modelizing the aerogel struc... more Phase transitions inside the pores of an aerogel are investigated by modelizing the aerogel structure by diffusion-limited cluster-cluster aggregation on a cubic lattice in a finite box and considering q-states Potts variables on the empty sites interacting via nearest-neighbours. Using a finite size scaling analysing of Monte-Carlo numerical results, it is concluded that for q = 4 the transition changes from first order to second order as the aerogel concentration (density) increases. Comparison is made with the case q = 3 (where the first order transition is weaker in three dimensions) and with the case q = 4 but for randomly (non correlated) occupied sites. Possible applications to experiments are discussed.

Physical Review Letters, 1995

ABSTRACT An aerogel of volume fraction c is modeled on a 3D lattice using diffusion-limited clust... more ABSTRACT An aerogel of volume fraction c is modeled on a 3D lattice using diffusion-limited cluster-cluster aggregation in cubic boxes of sizes up to 20×20×20. A set of q-state Potts variables are disposed on the nonoccupied sites and their order-disorder phase transition is studied by means of a Monte Carlo technique for q = 3 and q = 4. It is found that the transition changes from first to second order above a nonzero threshold value of c. A comparison is made with the case of randomly occupied sites. The possible application to recent experimental results is discussed.

The first-order phase transition in the one-dimensional q-state Potts model with long-range inter... more The first-order phase transition in the one-dimensional q-state Potts model with long-range interactions decaying with distance as 1 r 1 ¡ σ, has been studied by Monte Carlo numerical simulations for 0 ¢ σ £ 1 and integer values of q ¤ 2. On the basis of the finite-size scaling analysis of interface free energy ΔFL, specific heat and Binder’s fourth order cumulant, we obtain the first-order transition which occurs for σ below a threshold value σc ¥ q ¦. The subject of our study is the one-dimensional (1d) Potts model with ferromagnetic long-range (LR) interactions decaying with distance as 1 r 1 ¡ σ, defined by the Hamiltonian H §© ¨ ∑ i � j J � i ¨ j � 1 ¡ σ δ ¥ si � s j ¦ � (1) where J ¤ 0, si denotes the q-state Potts variable at site i, δ is the Kronecker symbol, and summation is taken over all pairs in the system. The phase transition at nonzero temperature, shown rigorously [1] for the Ising ¥ q § 2 ¦ case with σ £ 1 and by renormalization group for the continuous n-compon...

We examine the order of the phase transition in the Potts model by using the graph representation... more We examine the order of the phase transition in the Potts model by using the graph representation for the partition function, which allows treating a non-integer number of Potts states. The order of transition is determined by the analysis of the shape of the graph-weight probability distribution. The approach is illustrated on special cases of the one-dimensional Potts model with long-range interactions and on its mean-ÿeld limit.

We present the numerical study of the one-dimensional Potts model with power-law decaying ferroma... more We present the numerical study of the one-dimensional Potts model with power-law decaying ferromagnetic interactions. The largest cluster probability distribution is obtained by Monte Carlo simulations using the Swendsen-Wang cluster algorithm with cumulative probabilities. The ÿnite-size scaling analysis of the largest cluster is used to derive the critical behaviour in the non-classical regime of this model for various values of q. The models involving long-range interactions have an important role in describing many complex systems, from physics to economy or biology, but the equilibrium critical phenomena in these models are still not well understood and deserve further attention. We consider here the 1d Potts model with long-range interactions deÿned by the Hamiltonian

The effect of the quenched random dilution on the ferromagnetic transitions, in particular, the c... more The effect of the quenched random dilution on the ferromagnetic transitions, in particular, the conversion from the first-to second-order transition is discussed. The new results are presented for the diluted three-dimensional three-state Potts model. The critical exponents of the disorder-induced second-order phase transition are derived by the finite-size scaling analysis of the moments of the energy and the largest cluster, obtained from the Monte Carlo simulations.

We have performed exact analytical calculations of the cluster probability distribution and inter... more We have performed exact analytical calculations of the cluster probability distribution and interface free energy in the finite q-state Potts chains with interactions decaying with distance r as r^(1+sigma). By presenting the partition function in form of the polynomial in q, the advantage of using the Hamiltonian configurations compared with graph or connectivity approach was examined. Scaling analysis of the probability performed for large q (q >= 16) yields the first-order phase transition for 0 < sigma < 1.

The invaded cluster algorithm [1] is generalized [2] to the tricritical point on the example of 2... more The invaded cluster algorithm [1] is generalized [2] to the tricritical point on the example of 2d Potts model with annealed dilution. Self-regulating procedure that locates the tricritical point in the two-parameter space spanned by temperature and chemical potential of vacancies is constructed based on geometrical arguments. The tricritical point is identified as a simultaneous percolation of the Fortuin-Kastelyn cluster and the geometrical cluster consisting of vacancies and isolated spins. The tricritical values of parameters and concentration are presented for q=1, 2, 3 and found to be in a good agreement with the best known results [3]. Scaling properties of the percolating scaling cluster and related critical exponents are also derived. Based on the idea that effective correlation of vacancies is important at the tricritical point, we also examine alternative stopping rules within generalized IC algorithm, and possible extension to higher dimensions. [1] J. Machta, Y. S. Choi...