Equilibrium Phase Transitions in Coupled Map Lattices: A Pedestrian Approach

A class of piecewise linear coupled map lattices with simple symbolic dynamics is constructed. It can be solved analytically in terms of the statistical mechanics of spin lattices. The corresponding Hamiltonian is written down explicitly in terms of the parameters of the map. The approach follows the line of recent mathematical investigations. But the presentation is kept elementary so that phase transitions in the dynamical model can be studied in detail. Although the method works only for map lattices with repelling invariant sets some of the conclusions, i.e., the role of local curvature of the single site map and properties of the nearest neighbour coupling might play an important role for phase transitions in general dynamical systems.     

Phase Transitions in Traffic Models

It is suggested that the question of existence of a jamming phase transition in a broad class of single-lane cellular-automaton traffic models may be studied using a correspondence to the asymmetric chipping model. In models where such correspondence is applicable, jamming phase transition does not take place. Rather, the system exhibits a smooth crossover between free-flow and jammed states, as the car density is increased.     

Dynamic Opalescence upon Phase Transitions and in Inhomogeneous Systems

The temperature isofrequency dependences of Raman intensities are studied in a number of crystals (lithium tantalate, barium sodium niobate, barium titanate, and quartz) in the low-frequency range near the structural phase-transition points. In the case of ferroelectrics, poly- and single-domain single crystals are studied with a stationary electric field applied to the sample. A drastic increase in the intensity of the quasielastic (low-frequency) light scattering is found when approaching the phase-transition point. The studies are carried out for the 90° scattering geometry as well as at angles close to 180° (backscattering geometry). The anomalies of the quasielastic light scattering near the points of phase transition are observed in the latter case. The position of the maximum intensity of the isofrequency dependence on the temperature scale is found to be dependent on the frequency value = ₀ – (₀ and are the frequency of exciting radiation and the frequency to which the monochromator is tuned, respectively). A theory explaining satisfactorily the observed effect of dynamic opalescence near the phase-transition points in crystals is developed. The specific features of light scattering in an inhomogeneous medium as well as the dynamic properties of the model of such a medium in the form of periodically arranged microresonators are studied. Additional vibrational branches (superlattice vibrations) are shown to be formed in such a medium under certain conditions. These branches give rise to a central peak and strongly affect the characteristics of the structural phase transition depending on the microresonator dimensions. The observing conditions of the dynamic opalescence in inhomogeneous media by the isochronous spectroscopy technique upon pulsed laser excitation are analyzed.     

Entropy-Driven Phase Transitions in Multitype Lattice Gas Models

In multitype lattice gas models with hard-core interaction of Widom–Rowlinson type, there is a competition between the entropy due to the large number of types, and the positional energy and geometry resulting from the exclusion rule and the activity of particles. We investigate this phenomenon in four different models on the square lattice: the multitype Widom–Rowlinson model with diamond-shaped resp. square-shaped exclusion between unlike particles, a Widom–Rowlinson model with additional molecular exclusion, and a continuous-spin Widom–Rowlinson model. In each case we show that this competition leads to a first-order phase transition at some critical value of the activity, but the number and character of phases depend on the geometry of the model. We also analyze the typical geometry of phases, combining percolation techniques with reflection positivity and chessboard estimates.     

Critical Behaviors and Universality Classes of Percolation Phase Transitions on Two-Dimensional Square Lattice

We have investigated both site and bond percolation on two-dimensional lattice under the random rule and the product rule respectively. With the random rule, sites or bonds are added randomly into the lattice. From two candidates picked randomly, the site or bond with the smaller size product of two connected clusters is added when the product rule is taken. Not only the size of the largest cluster but also its size jump are studied to characterize the universality class of percolation. The finite-size scaling forms of giant cluster size and size jump are proposed and used to determine the critical exponents of percolation from Monte Carlo data. It is found that the critical exponents of both size and size jump in random site percolation are equal to that in random bond percolation. With the random rule, site and bond percolation belong to the same universality class. We obtain the critical exponents of the site percolation under the product rule, which are different from that of both random percolation and the bond percolation under the product rule. The universality class of site percolation differs different from that of bond percolation when the product rule is used.     

光学多稳系统的相变及临界点分类

参照朗道相变理的基本精神,确定光学多稳性系统的相变与临床界现象,揭示了相变的多样性,以及多稳系统通向完全单稳状态态的不同路径。多稳性的级次愈高,相变的式样也就愈多。     

Classification of Phase Transitions and Ensemble Inequivalence, in Systems with Long Range Interactions

Systems with long range interactions in general are not additive, which can lead to an inequivalence of the microcanonical and canonical ensembles. The microcanonical ensemble may show richer behavior than the canonical one, including negative specific heats and other non-common behaviors. We propose a classification of microcanonical phase transitions, of their link to canonical ones, and of the possible situations of ensemble inequivalence. We discuss previously observed phase transitions and inequivalence in self-gravitating, two-dimensional fluid dynamics and non-neutral plasmas. We note a number of generic situations that have not yet been observed in such systems.     

Coulombic Phase Transitions in Dense Plasmas

We give a survey on the predictions of Coulombic phase transitions in dense plasmas (PPT) and derive several new results on the properties of these transitions. In particular we discuss several types of the critical point and the spinodal curves of quantum Coulombic systems. We construct a simple theoretical model which shows (in dependence on the parameter values) either one alkali-type transition (Coulombic and van der Waals forces determine the critical point) or one Coulombic transition and another van der Waals transition. We investigate the conditions to find separate Van der Waals and Coulomb transitions in one system (typical for hydrogen and noble gas-type plasmas). The separated Coulombic transitions which are strongly influenced by quantum effects are the hypothetical PPT, they are in full analogy to the known Coulombic transitions in classical ionic systems. Finally we give a discussion of several numerical and experimental results referring to the PPT in high pressure plasmas.     

Thermal Phase Transitions of IOTA Carrageenan in CaCl2 Solutions: A Fluorescence Study

The fluorescence technique was employed to study thermal phase transitions of iota (ι-) carrageenan (IC) in CaCl₂ solution. IC gels underwent coil to double helix (c-h) and double helix to dimer (h-d) transitions upon cooling. Upon heating IC gels presented dimer to double helix (d-h) and double helix to coil (h-c) transitions, showing hysteresis types of transition paths. Scattered light, I_sc and fluorescence intensity, I, were monitored against temperature to determine phase transitions. Transition temperatures were determined from the derivative of the transition paths. The critical gel fraction exponent, β, was measured and found to be in accord with the classic Flory–Stockmayer model.     

Quantum Phase Transitions and Dimerized Phases in Frustrated Spin Ladder

In this paper, we study the phase diagram of a frustrated spin ladder model by applying the bosonization technique and the density-matrix renormalization-group (DMRG) algorithm. Effect of the intra-chain next-nearest-neighbor (NNN) super-exchange interaction is investigated in detail and the order parameters are calculated to detect the emergence of the dimerized phases. We find that the intra-chain NNN interaction plays a key role in inducing dimerized phases.     

QCD手征相变中的π介子增强(英文)

讨论了在LHC的Pb-Pb碰撞过程中,如果QGP SU(2)手征相变出现二级相变,那么系统将会有π弦产生,并且π弦最终将衰变为π介子。于是以上效应将导致在低动量区域（p~150—400 MeV）内的π介子增强。对应于不同的冷却温度T_f=130,120,110 MeV,产生于π弦衰变的π介子的数量分别是Nt≈270,150, 60. It is pointed out that if the QGP SU(2) chiral phase transition in the LHC Pb Pb collision process is taken place and the phase transition is in the second order, then pion strings will be formed, and decay. These phenomena lead to the pion enhancement in the low momentum region(p150—400 MeV) and the number of pions produced from pion string decay can be estimated about Nt≈270, 150, 60 for different freeze temperature Tf=130, 120, 110 MeV respectively.     

酯类铁电液晶的相变和构型研究(英文)

：本文对酯类铁电液晶的相变和构型进行了研究和评述。它包括固相 近晶Ｃ,近晶Ｃ 近晶Ａ相变的性质,一级、二级相变的判据,固相 近晶Ｃ相变的临界弛豫,顺式、反式的构型转变和新相分析。     

Dynamical Phase Transition in a Neural Network Model with Noise: An Exact Solution

The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same value. It is shown that, under very general conditions, there exists a critical value _c of the noise, below which the network remains organized and above which it behaves randomly. The existence and nature of the phase transition are computed analytically, showing that the critical exponent is 1/2. The dependence of _c on the parameters of the network is obtained. These results are then compared with two numerical realizations of the network.     

Peculiar Quantum Phase Transitions and Hidden Supersymmetry in a Lipkin-Meshkov-Glick Model

In this paper we theoretically report an unconventional quantum phase transition of a simple Lipkin- Meshkow-Glick model： an interacting collective spin system without external magnetic field. It is shown that this model with integer-spin can exhibit a flrst-order quantum phase transition between different disordered phases, and more intriguingly, possesses a hidden supersymmetry at the critical point. However, for half-integer spin we predict another flrst-order quantum phase transition between two different long-range-ordered phases with a vanishing energy gap, which is induced by the destructive topological quantum interference between the intanton and anti-instanton tunneling paths and accompanies spontaneously breaking of supersymmetry at the same critical point. We also show that, when the total spin-value varies from half-integer to integer this model can exhibit an abrupt variation of Berry phase from π to zero.     

Phase Transitions in a Mixture of Hard-Sphere Dipoles and Neutral Hard Spheres

Using the reference hypernetted chain （RHNC） integral equation theory and a rigorous stability analysis method, we investigate the phase behavior of a mixture of hard-sphere dipoles and neutral hard spheres based on the correlations of the homogeneous isotropic phase. Lowering the temperature down to the points where the RHNC equations fail to have a solution, several ttuctuations strongly increase. At low densities our results indicate the onset of ／ chain formation, which is similar with the pure DHS system. At high densities, the results indicate the appearance of isotropic-to-ferroelectric transitions （small neutral hard spheres concentrations） and demixing transitions （large neutral hard spheres concentrations）.     

SD对壳模型下原子核形状相变（英文）

在SD 对壳模型的理论框架下讨论了原子核形状相变模式。研究结果表明,该理论模型可以把相互作用玻色子模型中U（5）-SU（3）以及U（5）-SO（6） 形状相变模式再现出来,相互作用玻色子模型中有关临界点对称性的特征也可以很好地描述。本文同时也发现原子核从振动到转动的形状相变可以通过改变相互作用强度来实现。The nuclear shape phase transitional patterns were studied in the SD-pair shell model. The results show that the transitional patterns similar to the U(5)-SU(3) and U(5)-SO(6) transitions in the interacting boson model can be produced. The signatures of the critical point symmetry in the interacting boson model are also produced approximately. It is also found that the shape phase transitional pattern between vibration and rotation can also be produced by changing the interactional strength.     

Phase Transitions in a Mixture of Hard-Sphere Dipoles and Neutral Hard Spheres

Using the reference hypernetted chain (RHNC) integral equation theory and a rigorous stability analysis method, we investigate the phase behavior of a mixture of hard-sphere dipoles and neutral hard spheres based on the correlations of the homogeneous isotropic phase. Lowering the temperature down to the points where the RHNC equations fail to have a solution, several fluctuations strongly increase. At low densities our results indicate the onset of chain formation, which is similar with the pure DHS system. At highdensities, the results indicate the appearance of isotropic-to-ferroelectric transitions (small neutral hard spheres concentrations) and demixing transitions (large neutral hard spheres concentrations).     

Out-of-Time-Order Correlators and Quantum Phase Transitions in the Rabi and Dicke Models

The out-of-time-order correlators (OTOCs) is used to study the quantum phase transitions (QPTs) between the normal phase and the superradiant phase in the Rabi and few-body Dicke models with large frequency ratio of the atomic level splitting to the single-mode electromagnetic radiation field frequency. The focus is on the OTOC thermally averaged with infinite temperature, which is an experimentally feasible quantity. It is shown that the critical points can be identified by long-time averaging of the OTOC via observing its local minimum behavior. More importantly, the scaling laws of the OTOC for QPTs are revealed by studying the experimentally accessible conditions with finite frequency ratio and finite number of atoms in the studied models. The critical exponents extracted from the scaling laws of OTOC indicate that the QPTs in the Rabi and Dicke models belong to the same universality class.     

Fluctuations-Inclusive Approach to Phase Transitions in Binary Mixtures

The hierarchical reference theory of fluids (HRT) is applied to the study of the phase diagram of binary mixtures of simple fluids. This approach implements the renormalization group machinery into a liquid-state theory in order to systematically deal with the effect of long-range correlations which play a crucial role in the onset of criticality and phase separation. The effect of fluctuations is embodied in a partial differential equation (PDE) for the free energy of the mixture. Recently, a robust numerical algorithm has been developed which enabled us to integrate this PDE on a substantial density mesh even at low temperature, when the coexistence region spreads over most of the density– concentration plane.We have considered a model mixture of spherical particles interacting via a hard-core plus attractive tail potential, and adjusted the particle diameters ₁, ₂ and the strengths of the attractive interactions ₁₁, ₂₂, ₁₂ so as to mimic mixtures of simple fluids such as argon–krypton or neon–krypton. In the latter case the theory reproduces the occurrence of a minimum in the critical temperature (the so-called critical double point) and of immiscibility at high pressure. We have also studied the phase diagram of a symmetric mixture such that ₁= ₂ and ₁₁= ₂₂ as the ratio = ₁₂/ ₁₁ is varied. In particular, we find that, in agreement with the mean-field picture, by decreasing , a critical endpoint occurring at equal species concentration is turned into a tricritical point. An interesting feature of the HRT is that, whenever phase coexistence occurs, the conditions of phase equilibria are implemented by the theory itself, without any need of enforcing them a posteriori. This allows one to straightforwardly map the phase diagram and the critical lines of the mixture.