On the definition of phase transition

It is shown that there exists a phase transition associated with a singularity of the free energy for a model such that for all temperatures the equilibrium state is unique and thus stable with respect to boundary perturbations. It is also shown on this model that there exist phase transitions without symmetry breakdown, which can be related to a phase transition with symmetry breakdown on an equivalent model.     

Degeneracy induced scaling of the correlation length for periodic models

The broken symmetric phase of scalar models exhibits an infrared fixed point which is induced by the degenerate effective potential. The definition of the correlation length in the infrared regime enables us to determine the type of the phase transition in the model. It is shown that the massive sine-Gordon model exhibits a continuous, while the layered sine-Gordon model has an infinite order Kosterlitz–Thouless type phase transition.     

Percolation Phase Transitions from Second Order to First Order in Random Networks

We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER network at q = 1, which is characterized by a robust second order phase transition. When q = 0, this model recovers to the SC model which exhibits a first order phase transition. To study how the percolation phase transition changes from second order to first order with the decrease of the value of q from 1 to 0, the numerical simulations study the final vanishing moment of the each existing cluster except the N-cluster in the percolation process. For the continuous phase transition,it is shown that the tail of the graph of the final vanishing moment has the characteristic of the convexity. While for the discontinuous phase transition, the graph of the final vanishing moment possesses the characteristic of the concavity.Just before the critical point, it is found that the ratio between the maximum of the sequential vanishing clusters sizes and the network size N can be used to decide the phase transition type. We show that when the ratio is larger than or equal to zero in the thermodynamic limit, the percolation phase transition is first or second order respectively. For our model, the numerical simulations indicate that there exists a tricritical point qcwhich is estimated to be between0.2 qc 0.25 separating the two phase transition types.     

Phase transition in liquids with directed intermolecular bonding

Liquids with quasi-chemical bonding between molecules are described in terms of vertex model. It is shown that this bonding results in liquid–liquid phase transition, which takes place between phases with different mean density of intermolecular bonds. The transition may be suggested to be a universal phenomena for those liquids.     

Phase transitions in 2D and 3D non-Heisenberg ferromagnets with temperature-dependent anisotropy

A model of a non-Heisenberg ferromagnet is considered in which the single-ion anisotropy constant is linearly dependent on temperature. The conditions are found under which phase transitions occur in 2D and 3D non-Heisenberg ferromagnets as the temperature is varied. It is shown that, in the case where the biquadratic interaction is dominant, quadrupole states can occur in the system, which are specified by the orientation of the quadrupole moment. As the temperature is varied, a phase transition between quadrupole states can occur in 2D magnets. Depending on the ratios between the material constants, this transition can be either a second-order phase transition with the continuously changing orientation of the principal axes of the quadrupole moment tensor or a first-order phase transition with hysteresis through a state with a nonhomogeneous distribution of the principal axes of the quadrupole moment tensor. In 3D magnets, the phase transition between quadrupole states is of the first order with hysteresis. Phase diagrams of the system are constructed.     

Erdös Rényi随机网络上爆炸渗流模型相变性质的数值模拟研究

基于改进的Newman和Ziff算法以及有限尺寸标度理论, 通过对表征渗流相变特征物理量的序参量、平均集团尺寸、二阶矩、标准偏差及尺寸不均匀性的数值模拟, 分析研究了Erdös Rényi随机网络上Achlioptas爆炸渗流模型的相变性质.研究表明: 尽管序参量表现出了不连续相变的特征, 但序参量以及其他特征物理量仍具有连续相变的幂律标度行为.因此严格地说, Erdös Rényi随机网络中的爆炸渗流相变是一种奇异相变, 它既不是标准的不连续相变, 又与常规随机渗流表现出的连续相变处于不同的普适类. 关键词： Erdös Rényi随机网络 爆炸渗流模型 相变 幂律标度行为     

Phase transitions in the Falicov–Kimball model away from half-filling

The canonical Monte Carlo method is used to study the order-disorder phase transition of the Falicov–Kimball model away from half-filling. It is shown that the transition from various inhomogeneous ground-state phases to the disordered phase can be either direct or indirect. The indirect transition means that the ground-state phase first, at critical temperature τ _c , changes to a different ordered phase and at the temperature, that can be several times higher than τ _c , finally changes to the disordered phase. It is shown that the Falicov–Kimball model, depending on the ground state phase, undergoes first order or second order phase transition or can even undergo both for the same parameters and different temperatures if the transition from the ground-state phase to the disordered phase is indirect.     

One-dimensional Bose-Hubbard model with pure three-body interactions

The extended Bose-Hubbard model with pure three-body local interactions is studied using the Density Matrix Renormalization Group approach. The shapes of the first two insulating lobes are discussed, and the values of the critical tunneling for which the system undergoes the quantum phase transition from insulating to superfluid phase are predicted. It is shown that stability of insulating phases, in contrast to the standard Bose-Hubbard model, is enhanced for larger fillings. It is also shown that, on the tip of the boundary of the insulating phase, the model under consideration belongs to the Berenzinskii-Kosterlitz-Thouless universality class.     

Phase transition in multiprocessor scheduling

An "easy-hard" phase transition is shown to characterize the multiprocessor scheduling problem in which one has to distribute the workload on a parallel computer such as to minimize the overall run time. The transition can be analyzed in detail by mapping it on a mean-field antiferromagnetic Potts model. The static phase transition, characterized by a vanishing ground state entropy, corresponds to a transition in the performance of practical scheduling algorithms.     

Lawrence–Doniach model in London approximation as a system of 2D Coulomb particles of two kinds

Thermodynamical properties of layered superconductors with Josephson coupling in zero magnetic field are discussed. It is shown that the Lawrence–Doniach model of layered superconductors in the London approximation can be presented as a system of classical Coulomb particles of two kinds. This representation includes both Josephson and 2D vortex subsystems in absolutely symmetrical way. The model was analyzed by means of the real-space renormalization group approach and in the mean field approximation. It is found that there is no a second order phase transition in the system. Instead of this the model demonstrates the qualitative change of the system properties which can look as a phase transition for experimental purposes.     

一类新的Stückelberg全息超导模型

本文研究了含Stückelberg机理的黑洞全息超导模型. 通过选取标量场新的高阶修正形式, 建立了新的Stückelberg黑洞全息超导模型. 通过研究模型参数对标量场凝聚的影响, 发现了当模型参数大于临界值时, 高阶修正可以引起一阶相变. 同时本文还考查了反作用对临界值的影响.     

Two-speed phase dynamics in the si(111) (7 x7)-(1 x 1) phase transition

We propose a natural two-speed model for the phase dynamics of Si(111) 7 x 7 phase transition to high-temperature unreconstructed phase. We formulate the phase dynamics by using phase-field method and adaptive mesh refinement. Our simulated results show that a 7 x 7 island decays with its shape kept unchanged, and its area decay rate is shown to be a constant increasing with its initial area. Low-energy electron microscopy experiments concerned are explained, which confirms that the dimer chains and corner holes are broken first in the transition, and then the stacking fault is remedied slowly. This phase-field method is a reliable approach to phase dynamics of surface phase transitions.     

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     

Self-trapping phase diagram for the strongly correlated extended Holstein-Hubbard model in two-dimensions

The two-dimensional extended Holstein-Hubbard model is investigated in the strong correlation regime to study the nature of self-trapping transition and the polaron phase diagram in the absence of superconductivity. Using a series of canonical transformations followed by zero-phonon averaging the extended Holstein-Hubbard model is converted into an effective extended Hubbard model which is subsequently transformed into an effective t-J model in the strong correlation limit. This effective t-J model is finally solved using the mean-field Hartree-Fock approximation to show that the self-trapping transition is continuous in the anti-adiabatic limit while it is discontinuous in the adiabatic limit. The phase diagrams for the localization-delocalization transition, namely the phase line and the phase surface separating the small polaron and large polaron states are also shown.     

First-order phase transition through an intermediate state

The theory of first-order phase transitions in systems where the direct formation of nuclei of a new phase is inhibited for any reason, for example, because of the extremely high elastic energy, has been constructed using the example of the silicon-silicon carbide phase transition due to the chemical reaction with carbon monoxide. It has been shown that, in this case, the phase transition occurs through an intermediate state, which significantly promotes the formation of new-phase nuclei. For the silicon-silicon carbide phase transition, such an intermediate state is the “pre-carbide” state of silicon saturated with dilatation dipoles, i.e., pairs formed by a carbon atom and a silicon vacancy that are strongly attracted to each other. The model dependence of the potential energy of systems with an intermediate phase on the reaction coordinates has been investigated. The kinetics of transformation of the intermediate state into a new phase has been described.     

Phase transition in the generalized Ising-Kosterlitz-Thouless model

The features of the phase transition are considered in a model that is a combination of the Ising and Kosterlitz-Thouless models. It is shown that one or two successive phase transitions may occur in such a system, depending on the relation between parameters. An asymptotic formula is derived for the Ising-type phase transition temperature.     

Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field

We consider a one-dimensional Ising model in a transverse magnetic field coupled to a dissipative heat bath. The phase diagram and the critical exponents are determined from extensive Monte Carlo simulations. It is shown that the character of the quantum phase transition is radically altered from the corresponding nondissipative model and the double well coupled to a dissipative heat bath with linear friction. Spatial couplings and the dissipative dynamics combine to form a new quantum criticality which is independent of dissipation strength.     

The spontaneous coherent state transition in the ϕ4-field model with an image mass

It is shown, that in the ?⁴-field model with an image mass (μ²<0) the phase transition is a spontaneous coherent state (SCS) phase transition. The connection between the spontaneous symmetry breaking, the coherent state and the phenomenological Ginzburg-Landau theory is shown.     

Phase transition in a three-states reaction-diffusion system

A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and annihilation of particles. It has been shown that the model undergoes a continuous phase transition from a phase where the currents of different species of particles are equal to another phase in which they are different. The total density of particles and also their currents in each phase are calculated exactly.