Critical phenomena Research Papers - Academia.edu (original) (raw)
Aligned stacks of monomethyl and dimethyl dimyristoyl phosphatidylethanolamine (DMPE) lipid bilayers, like the much studied dimyristoyl PC (DMPC) bilayers, swell anomalously in a critical fashion as the temperature is decreased within the... more
Aligned stacks of monomethyl and dimethyl dimyristoyl phosphatidylethanolamine (DMPE) lipid bilayers, like the much studied dimyristoyl PC (DMPC) bilayers, swell anomalously in a critical fashion as the temperature is decreased within the fluid phase towards the main transition temperature, T(M). Unlike DMPC bilayers, both monomethyl and dimethyl DMPE undergo transitions into a gel phase rather than a rippled phase below T(M). Although it is not fully understood why there is anomalous swelling, our present results should facilitate theory by showing that the formation of the phase below T(M) is not related to critical phenomena above T(M).
The emergence of self-similarity and modularity in complex networks raises the fun- damental question of the growth process according to which these structures evolve. The possibility of a unique growth mechanism for biological networks,... more
The emergence of self-similarity and modularity in complex networks raises the fun- damental question of the growth process according to which these structures evolve. The possibility of a unique growth mechanism for biological networks, WWW and the Internet is of interest to the specialist and the laymen alike, as it promises to uncover the universal origins of collective behavior. Here,
We study self-organization of collective motion as a thermodynamic phenomenon in the context of the first law of thermodynamics. It is expected that the coherent ordered motion typically self-organises in the presence of changes in the... more
We study self-organization of collective motion as a thermodynamic phenomenon in the context of the first law of thermodynamics. It is expected that the coherent ordered motion typically self-organises in the presence of changes in the (generalized) internal energy and of (generalized) work done on, or extracted from, the system. We aim to explicitly quantify changes in these two quantities in a system of simulated self-propelled particles and contrast them with changes in the system's configuration entropy. In doing so, we adapt a thermodynamic formulation of the curvatures of the internal energy and the work, with respect to two parameters that control the particles' alignment. This allows us to systematically investigate the behavior of the system by varying the two control parameters to drive the system across a kinetic phase transition. Our results identify critical regimes and show that during the phase transition, where the configuration entropy of the system decreases, the rates of change of the work and of the internal energy also decrease, while their curvatures diverge. Importantly, the reduction of entropy achieved through expenditure of work is shown to peak at criticality. We relate this both to a thermodynamic efficiency and the significance of the increased order with respect to a computational path. Additionally, this study provides an information-geometric interpretation of the curvature of the internal energy as the difference between two curvatures: the curvature of the free entropy, captured by the Fisher information, and the curvature of the configuration entropy.
Our aim in this set of lectures is to give an introduction to critical phenomena that emphasizes the emergence of and the role played by diverging length-scales. It is now accepted that renormalization group gives the basic understanding... more
Our aim in this set of lectures is to give an introduction to critical phenomena that emphasizes the emergence of and the role played by diverging length-scales. It is now accepted that renormalization group gives the basic understanding of these phenomena and so, instead of following the traditional historical trail, we try to develop the subject in a way that emphasizes the length-scale based approach.
1. Algebraic Preliminaries. 2. Euclidean Path Integrals in Quantum Mechanics. 3. Path Integrals in Quantum Mechanics: Generalizations. 4. Stochastic Differential Equatons: Langevin, Fokker-Planck Equations. 5. Path and Functional... more
1. Algebraic Preliminaries. 2. Euclidean Path Integrals in Quantum Mechanics. 3. Path Integrals in Quantum Mechanics: Generalizations. 4. Stochastic Differential Equatons: Langevin, Fokker-Planck Equations. 5. Path and Functional Integrals in Quantum Statistical Physics. ...
Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following non-trivial power laws in experimentally relevant distributions. Previous numerical... more
Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following non-trivial power laws in experimentally relevant distributions. Previous numerical estimates on the critical exponents, when existing, are confirmed and superseded. A physical motivation for both models in the present framework is also discussed.
Description/Abstract The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly... more
Description/Abstract The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by ...
We develop a thermodynamic formalism for a dissipative version of the Zhang model of Self-Organized Criticality, where a parameter allows us to tune the local energy dissipation. By constructing a suitable Markov partition we define Gibbs... more
We develop a thermodynamic formalism for a dissipative version of the Zhang model of Self-Organized Criticality, where a parameter allows us to tune the local energy dissipation. By constructing a suitable Markov partition we define Gibbs measures (in the sense of Sinai, Ruelle, and Bowen), partition functions, and topological pressure allowing the analysis of probability distributions of avalanches. We discuss the infinite-size limit in this setting. In particular, we show that a Lee-Yang phenomenon occurs in the conservative case. This suggests new connections to classical critical phenomena.
We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche... more
We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions.
We summarize basic features associated to dynamical breaking of the electroweak symmetry. The knowledge of the phase diagram of strongly coupled theories as function of the number of colors, flavors and matter representation plays a... more
We summarize basic features associated to dynamical breaking of the electroweak symmetry. The knowledge of the phase diagram of strongly coupled theories as function of the number of colors, flavors and matter representation plays a fundamental role when trying to construct viable extensions of the standard model (SM). Therefore we will report on the status of the phase diagram for SU(N) gauge theories with fermionic matter transforming according to arbitrary representations of the underlying gauge group. We will discuss how the phase diagram can be used to construct unparticle models. We will then review Minimal Walking Technicolor (MWT) and other extensions, such as partially gauged and split technicolor. MWT is a sufficiently general, symmetry wise, model to be considered as a benchmark for any model aiming at breaking the electroweak symmetry dynamically. The unification of the standard model gauge couplings will be revisited within technicolor extensions of the SM. A number of appendices are added to review some basic methods and to provide useful details. In one of the appendices we will show how to gain information on the spectrum of strongly coupled theories relevant for new extensions of the SM by introducing and using alternative large N limits.
All higher-spin (s≥1/2) Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3, exactly on a d=3 hierarchical model and, simultaneously, by the Migdal-Kadanoff approximation on the cubic lattice. The... more
All higher-spin (s≥1/2) Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3, exactly on a d=3 hierarchical model and, simultaneously, by the Migdal-Kadanoff approximation on the cubic lattice. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found that, in d=3, a finite-temperature spin-glass phase occurs for all spin values, including the continuum limit of s→∞. The phase diagrams, with increasing spin s, saturate to a limit value. The spin-glass phase, for all s, exhibits chaotic behavior under rescalings, with the calculated Lyapunov exponent of λ=1.93 and runaway exponent of yR=0.24, showing simultaneous strong-chaos and strong-coupling behavior. The ferromagnetic-spin-glass and spin-glass-antiferromagnetic phase transitions occurring, along their whole length, respectively at pt=0.37 and 0.63 are unaffected by s, confirming the percolative nature of this phase transition.
Critical behavior occurs at \mu\ell=3, where the warping transitions from a stretching to a squashing, and there are a pair of warped solutions with a null U(1) isometry. For \mu\ell>3, there are known warped black hole solutions which... more
Critical behavior occurs at \mu\ell=3, where the warping transitions from a stretching to a squashing, and there are a pair of warped solutions with a null U(1) isometry. For \mu\ell>3, there are known warped black hole solutions which are asymptotic to warped AdS_3. We show that these black holes are discrete quotients of warped AdS_3 just as BTZ black holes are discrete quotients of ordinary AdS_3. Moreover new solutions of this type, relevant to any theory with warped AdS_3 solutions, are exhibited. Finally we note that the black hole thermodynamics is consistent with the hypothesis that, for \mu\ell>3, the warped AdS_3 ground state of TMG is holographically dual to a 2D boundary CFT with central charges c_R={15(\mu\ell)^2+81\over G\mu((\mu\ell)^2+27)} and c_L={12 \mu\ell^2\over G((\mu\ell)^2+27)}.
We deduce the qualitative phase diagram of a long flexible neutral polymer chain immersed in a poor solvent near an attracting surface using phenomenological arguments. The actual positions of the phase boundaries are estimated... more
We deduce the qualitative phase diagram of a long flexible neutral polymer chain immersed in a poor solvent near an attracting surface using phenomenological arguments. The actual positions of the phase boundaries are estimated numerically from series expansion up to 19 sites of a self-attracting self-avoiding walk in three dimensions. In two dimensions, we calculate phase boundaries analytically in some cases for a partially directed model. Both the numerical and analytical results corroborate the proposed qualitative phase diagram.
In this paper we study the short-time behavior of the Blume-Capel model at the tricritical point as well as along the second order critical line. Dynamic and static exponents are estimated by exploring scaling relations for the... more
In this paper we study the short-time behavior of the Blume-Capel model at the tricritical point as well as along the second order critical line. Dynamic and static exponents are estimated by exploring scaling relations for the magnetization and its moments at early stage of the dynamic evolution. Our estimates for the dynamic exponents, at the tricritical point, are z=2.215(2)z= 2.215(2)z=2.215(2) and theta=−0.53(2)\theta= -0.53(2)theta=−0.53(2).