Inhomogeneous Ising models with diagonal structure on a square lattice

We study inhomogeneous Ising models on a square lattice. The nearest neighbour couplings are allowed to be of arbitrary strength and sign such that the coupling distribution is translationally invariant in diagonal direction. We calculate the partition function and free energy for a random coupling distribution of finite period. The phase transition is universally of Ising type. The transition temperature is independent of specific details of the coupling distribution. In particular, unexpected results for the absence of a phase transition are derived. Special examples are considered in detail, phase diagrams and critical temperature are determined. We calculate ground state energy and ground state degeneracy or, equivalently, rest entropy for “pure” frustration models, i.e. models with couplings of fixed strength but arbitrary sign, which never show a phase transition at a finite temperature.     

Coherent potential approximation study of the Mott transition in optical lattice system with site-dependent interactions

We study the Mott transition in the half-filled Hubbard model with spatially alternating interactions by means of the coherent potential approximation. The phase boundary between metallic and insulating phases at zero temperature is derived and the nature of the Mott states is also considered. Our results are in good agreement with the ones recently obtained by the two-site dynamical mean-field theory.     

Phase transitions induced by saddle points of vanishing curvature

Based on the study of saddle points of the potential energy landscapes of generic classical many-particle systems, we present a necessary criterion for the occurrence of a thermodynamic phase transition. Remarkably, this criterion imposes conditions on microscopic properties, namely, curvatures at the saddle points of the potential, and links them to the macroscopic phenomenon of a phase transition. We apply our result to two exactly solvable models, corroborating that the criterion derived is not only valid, but also sharp and useful: For both models studied, the criterion excludes the occurrence of a phase transition for all values of the potential energy but the transition energy. This result adds a geometrical ingredient to an established topological condition for the occurrence of a phase transition, thereby providing an answer to the long-standing question of which topology changes in configuration space can induce a phase transition.     

Statistical mechanics of melting mediated by two types of defects

We propose a defect-mediated melting theory based on the statistics of two types of lattice defects, the point defects and dislocation pairs. The model predicts a first-order phase transition. Based on the model, phase transition temperature, latent heat and other thermodynamic functions are derived. Melting occurs due to discontinuous growth of point defects into dislocation pairs. The calculated phase transition temperature for five alkali metallic crystals are in fair agreement with measured melting temperatures, and the Richards' rule is derived by the model also.     

Inhomogeneous Ising models with diagonal structure on a square lattice

We study inhomogeneous Ising models on a square lattice. The nearest neighbour couplings are allowed to be of arbitrary strength and sign such that the coupling distribution is translationally invariant in diagonal direction. We calculate the partition function and free energy for a random coupling distribution of finite period. The phase transition is universally of Ising type. The transition temperature is independent of specific details of the coupling distribution. In particular, unexpected results for the absence of a phase transition are derived. Special examples are considered in detail, phase diagrams and critical temperature are determined. We calculate ground state energy and ground state degeneracy or, equivalently, rest entropy for pure frustration models, i.e. models with couplings of fixed strength but arbitrary sign, which never show a phase transition at a finite temperature.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln, FRG     

中子星内部强子-夸克相变的有限尺度效应研究

在致密星体内部极高密度条件下,强子物质可能发生退禁闭相变成为夸克物质,即强子-夸克相变。这种相变过程对于中子星的性质有着重要影响。考虑库仑能和表面能的影响,即有限尺度效应,相变过程中的混杂相包含了被称为pasta相的几何结构。强子-夸克共存相的平衡条件是通过求总能量的最小值得到的。采用相对论平均场（RMF）模型来描述强子物质相,采用Nambu-Jona-Lasinio（NJL）模型来描述夸克物质相。有限尺度效应一定程度上增加了中子星的最大质量,增加幅度取决于强子-夸克表面张力的大小。有限尺度效应能够降低混杂相的范围,其结果介于Gibbs结构和Maxwell结构的结果之间。研究结果表明,中子星中可能包含一个混杂相的核心部分,其大小受到表面张力等参数的影响。It is generally considered that hadron matter may undergo a deconfinement phase transition becoming quark matter at very high density in massive neutron stars. This hadron-quark phase transition has important impact on neutron stars, which has received much attention. We consider finite-size effect in this phase transition process, which contains the impact of Coulomb energy and surface energy. By including this effect, the mixed phase forms the pasta structures. The equilibrium conditions for coexisting hadronic and quark phases are derived by minimizing the total energy including the surface and Coulomb contributions. We employ the relativistic mean-field(RMF) model to describe the hadronic phase, while the Nambu-Jona-Lasinio(NJL) model is used for the quark phase. We conclude that the finite-size effect will raise the stiffness of EOS, and then increase the maximum mass of neutron stars, which depend on the value of surface tension. Our results show that finite-size effects can significantly reduce the region of the mixed phase, and the results lie between those from the Gibbs and Maxwell constructions. We show that a massive star may contain a mixed phase core and its size depends on the surface tension of the hadron-quark interface.     

Holographic Insulator/Superconductor Phase Transition in Born-Infeld Electrodynamics

We study holographic insulator/superconductor phase transition in the framework of Born-Infeld electrodynamics both numerically and analytically. First we numerically study the effects of the Born-Infeld electrodynamics on the phase transition, find that when the Born-Infeld parameter increases, the critical chemical potential keeps invariant but the gap frequency becomes larger. Then we employ the variational method for the Sturm-Liouville eigenvalue problem to study the phase transition analytically. The analytical results obtained are found to be consistent with the numerical results.     

Freezing transition in the mean-field approximation model of pedestrian counter flow

We study the freezing transition in the counter flow of pedestrians within the channel numerically and analytically. We present the mean-field approximation (MFA) model for the pedestrian counter flow. The model is described in terms of a couple of nonlinear difference equations. The excluded-volume effect and bi-directionality are taken into account. The fundamental diagrams (current-density diagrams) are derived. When pedestrian density is higher than a critical value, the dynamical phase transition occurs from the free flow to the freezing (stopping) state. The critical density is derived by using the linear stability analysis. Also, the velocity and current (flow) at the steady state are derived analytically. The analytical result is consistent with that obtained by the numerical simulation.     

Freezing of random RNA

We study secondary structures of random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder. We show that there is a continuous phase transition from a molten phase at higher temperatures to a low-temperature glass phase. The primary freezing occurs above the critical temperature, with local islands of stable folds forming within the molten phase. The size of these islands defines the correlation length of the transition. Our results include critical exponents at the transition and in the glass phase.     

O(n) model on the honeycomb lattice via reflection matrices: Surface critical behaviour

We study the O(n) loop model on the honeycomb lattice with open boundary conditions. Reflection matrices for the underlying Izergin-Korepin R-matrix lead to three inequivalent sets of integrable boundary weights. One set, which has previously been considered, gives rise to the ordinary surface transition. The other two sets correspond respectively to the special surface transition and the mixed ordinary-special transition. We analyse the Bethe ansatz equations derived for these integrable cases and obtain the surface energies together with the central charges and scaling dimensions characterizing the corresponding phase transitions.     

Dynamics of Bose–Einstein condensate in driven tilted optical lattices

We study the dynamics of Bose–Einstein condensate in one-dimensional driven tilted periodic optical lattices by using variational approximation and numerical simulation. Rich phenomena are revealed, including diffusion, self-trapping, breather and soliton, which strongly depend on the atomic interaction, the amplitude of the modulation, the constant force and the phase difference between the Bloch oscillations and the drive. The critical conditions for the dynamical transition from diffusion to self-trapping and for the formation of the soliton are derived analytically. In addition, the phase diagrams of dynamical transitions are presented in full parameters space. We find that the dynamics of the system can be completely controlled by adjusting the constant force, the amplitude of the modulation and the phase difference between the Bloch oscillations and the drive. The results are confirmed by the direct numerical simulation of the full Gross–Pitaevskii equation.     

Interplay of exchange and electromagnetic effects in the coexistence of superconductivity and helical spin order

A correct Ginzburg-Landau free-energy functional for exchange (EX) and electromagnetic (EM) effects in a magnetic superconductor is derived. We study the second-order transition from the superconducting phase to the superconducting phase with helical spin order. The temperature T_M of the onset of the helical ordering and the wave vector of the helix Q are calculated for some cases.     

Canonical Entropy and Phase Transition of Rotating Black Hole

Recently, the Hawking radiation of a black hole has been studied using the tunnel effect method. The radiation spectrum of a black hole is derived. By discussing the correction to spectrum of the rotating black hole, we obtain the canonical entropy. The derived canonical entropy is equal to the sum of Bekenstein-Havcking entropy and correction term. The correction term near the critical point is different from the one near others. This difference plays an important role in studying the phase transition of the black hole. The black hole thermal capacity diverges at the critical point. However, the canonical entropy is not a complex number at this point. Thus we think that the phase transition created by this critical point is the second order phase transition. The discussed black hole is a five-dimensional Kerr-AdS black hole. We provide a basis for discussing thermodynamic properties of a higher-dimensional rotating black hole.     

First and second order transition in frustrated XY systems

The nature of the phase transition for the XY stacked triangular antiferromagnet (STA) is a controversial subject at present. The field theoretical renormalization group (RG) in three dimensions predicts a first order transition. This prediction disagrees with Monte-Carlo (MC) simulations which favor a new universality class or a tricritical transition. We simulate by the Monte-Carlo method two models derived from the STA by imposing the constraint of local rigidity which should have the same critical behavior as the original model. A strong first order transition is found. Following Zumbach we analyze the second order transition observed in MC studies as due to a fixed point in the complex plane. We review the experimental results in order to clarify the critical behavior observed. Received: 18 February 1998 / Revised: 24 April 1998 / Accepted: 30 April 1998     

CRITICAL SCALING THEORY OF GENERALIZED PHASE TRANSITION AND ITS UNIVERSALITY

Generalized phase transition (GPT) refers to the transition process of material systems from one steady-state to another. It includes equilibrium phase transition (EPT) and nonequilibrium phase transition (NPT), and phase transitions intermediate between them. In this paper some results on the study of critical scaling relations of the NPT and EPT are obtained. We developed the critical scaling theory of EPT and advanced a universal critical scaling theory of GPT. The critical scaling relations(scaling laws) has more niversality. The critical exponents calculated from our theory are identical with the results of experiments and other theories about EPT and NPT systems. Because the basic model of the theory does not depend on the concrete material system, it has a certain unversality. Its results thus can be applied to generlized phase transition systems, such as the electrorheological fluid and magnetorheological fluid systems.     

Chiral phase transition at finite temperature in the linear sigma model

We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength. Recieved: 19 September 1997 / Revised version: 30 October 1997     

The flux-tube phase transition and bound states at high temperatures

We consider the phase transition in the dual Yang-Mills theory at finite temperature T. The phase transition is associated with a change (breaking) of symmetry. The effective mass of the dual gauge field is derived as a function of the T-dependent gauge coupling constant. We investigate the analytical criterion constraining the existence of a quark-antiquark bound state at temperatures higher than the temperature of deconfinement. The text was submitted by the author in English.     

Noise-Induced Phase Transition: Zero-Dimensional Brownian Particles Varying between Ergodicity and Nonergodicity

We study in phase space a zero-dimensional system of Brownian particles which move in a periodic potential and subject to an internal time derivative Ornstein-Uhlenbeck noise. To resolve the Fokker-Planck equation in such a case, we propose an approximate analytical method. The theoretical predictions exhibit a second order noise-induced nonequilibrium phase transition, which is confirmed by numerical simulation results. The phase transition brings the system from an ergodicity to a nonergodicity phase as the potential barrier height decreases.     

Phase structure of two-flavor QCD at finite chemical potential

We study the phase diagram of two-flavor QCD at imaginary chemical potentials in the chiral limit. To this end we compute order parameters for chiral symmetry breaking and quark confinement. The interrelation of quark confinement and chiral symmetry breaking is analyzed with a new order parameter for the confinement phase transition. We show that it is directly related to both the quark density as well as the Polyakov loop expectation value. Our analytical and numerical results suggest a close relation between the chiral and the confinement phase transition.