Phase transition in the lattice gross-neveu model

The confining properties of the leading logarithm approximation to the effective lagrangian $\text{L}\text{= F}{}^2\text{/2g}{}^2\text{(t)}$ [ with g(t) a running coupling function of t = log(F²/μ⁴)] are seen to disappear when the second and the third approximations of the β-function power series expansion are considered.     

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 transition model for community detection

Motivated by social and biological interactions, a novel type of phase transition model is provided in order to investigate the emergence of the clustering phenomenon in networks. The model has two types of interactions: one is attractive and the other is repulsive. In each iteration, the phase of a node (or an agent) moves toward the average phase of its neighbors and moves away from the average phase of its non-neighbors. The velocities of the two types of phase transition are controlled by two parameters, respectively. It is found that the phase transition phenomenon is closely related to the topological structure of the underlying network, and thus can be applied to identify its communities and overlapping groups. By giving each node of the network a randomly generated initial phase and updating these phases by the phase transition model until they reach stability, one or two communities will be detected according to the nodes’ stable phases, confusable nodes are moved into a set named _Of$O_f$. By removing the detected communities and the nodes in _Of$O_f$, another one or two communities will be detected by an iteration of the algorithm, …. In this way, all communities and the overlapping nodes are detected. Simulations on both real-world networks and the LFR benchmark graphs have verified the efficiency of the proposed scheme.     

A molecular dynamics model for nuclear clusterization

We present a newly developed Nuclear Molecular Dynamics model aiming at the dynamical simulations of intermediate-energy heavy-ion collisions. This is a quasi-classical approach reducing a complex many-body dynamics to the propagation of Gaussian nucleons in a nuclear mean field and stochastic two-body scattering. We describe in detail main ingredients of the model including the Hamiltonian, scattering algorithm and initialization procedure. We show how the model describes isolated nuclei and the nuclear matter equation of state. The limitation of the model in reproducing the fermionic nature of nuclei is also demonstrated. The main emphasis in the paper is put on the study of the fragment formation dynamics. The backtracing method is applied to investigate the time evolution of subsets of nucleons which finally organize themselves into clusters. The non-equilibrium features of the clusterization process are demonstrated by several examples.     

Phase transition properties for the kinetic Ising model in an oscillating magnetic field

The phase transition properties for the kinetic Ising model in a sinusoidally oscillating magnetic field are investigated by means of the mean-field calculations. The integrated phase diagrams for not only the amplitude of the oscillating field versus temperature but also the frequency of the oscillating field versus temperature have been calculated respectively, in which the discontinuous and continuous transitions are observed. Meanwhile the hysteresis loops in relation to the two kinds of the phase diagrams have been analyzed systematically, and the effects of the amplitude and the frequency of the oscillating field on the hysteresis loops are illustrated.     

Phase transition in gauge theories and multiple-point model

The phase transition in the regularized U(1) gauge theory is investigated by using the dual Abelian Higgs model of scalar monopoles. The corresponding-renormalization-group-improved effective potential, analogous to the Coleman-Weinberg one, is considered in the two-loop approximation for β functions, and the phase-transition (critical) dual and nondual couplings are calculated in the U(1) gauge theory. It is shown that the critical value of the renormalized electric fine-structure constant,α _crit≈0.208, obtained in this study agrees with the lattice result for compact QED: α _crit ^lat ≈0.20±0.015. This result and the behavior of α in the vicinity of the phase-transition point are compared with the multiple-point-model prediction for the values of α near the Planck scale. Such a comparison is very encouraging for the multiple point model assuming the existence of the multiple critical point at the Planck scale.     

Phase transition in an occupationally disordered sulfate system

We have investigated the behavior of the Li_1.43Cs_0.57SO₄ single-crystal Raman spectra and dielectric permittivity as a function of temperature. It was observed that the crystal, which is an occupationally disordered system, with orthorhombic C_2v² structure at room temperature, undergoes a phase transition at 230 K. In the new phase the SO₄ tetrahedra remain in two non-equivalent sites and there is no evidence of the doubling of the unit cell.     

Phase transition in a mean-field model for sympatric speciation

We introduce an analytical model for population dynamics with intra-specific competition, mutation and assortative mating as basic ingredients. The set of equations that describes the time evolution of population size in a mean-field approximation may be decoupled. We find a phase transition leading to sympatric speciation as a parameter that quantifies competition strength is varied. This transition, previously found in a computational model, occurs to be of first order.     

Phase transition in the spanning-hyperforest model on complete hypergraphs

By using our novel Grassmann formulation we study the phase transition of the spanning-hyperforest model of the k-uniform complete hypergraph for any k2. The case k=2 reduces to the spanning-forest model on the complete graph. Different k are studied at once by using a microcanonical ensemble in which the number of hypertrees is fixed. The low-temperature phase is characterized by the appearance of a giant hyperforest. The phase transition occurs when the number of hyperforests is a fraction (k−1)/k of the total number of vertices. The behaviour at criticality is also studied by means of the coalescence of two saddle points. As the Grassmann formulation exhibits a global supersymmetry we show that the phase transition is second order and is associated to supersymmetry breaking and we explore the pure thermodynamical phase at low temperature by introducing an explicit breaking field.     

Phase transition in a generalized Dicke model of superradiance

By means of the use of the “gap equations”, we calculate the thermodynamic properties of a sufficiently general Dicke model. We obtain the general relations which correspond to the condition of second-order phase transition from the normal to the superradiant state.     

Phase transition in the Jacobsen-Stevens model of spin-lattice systems

The thermodynamic properties of the Jacobsen-Stevens model for spins coupled to lattice are considered. It is shown that for a sufficiently large value of the coupling constant between the spins and the phonons, the system exhibits a second-order phase transition at a certain critical temperature. Calculations are also made for averages of phonon number and spin. An estimate of critical temperature is given for the resonant case.     

Phase transition in an ideal bose gas in an external field

Bose-Einstein condensation is analyzed in an ideal Bose gas in an external field at temperatures at which the energy spectrum can be assumed continuous. The nature of the phase transition depends on the behavior of the potential near its minima. Criteria are derived which show in which fields the condensation is a second-order phase transition, a third-order phase transition with an infinite discontinuity in C_V/T, or a third-order phase transition with a finite discontinuity in C_V/T.Translated from Izvestiya VUZ. Fizika, No. 5, pp. 110–114, May, 1971.     

一维 Frenkel-Kontorova(FK)模型原子链的相变研究

文章基于一维Frenkel-Kontorova模型,研究了边界原子的初始速度对原子链运动状态的影响,数值模拟结果表明:当v1时,原子处于"振荡区",当v₁2时,原子处于"混沌区",当v>v₂时,原子处于 "均匀区". 同时我们发现临界速度v₁和v₂随原子数目和垫底势高度的变化而变化. 关键词： Frenkel-Kontorova(FK)模型 相变     

Phase transition in the 3d random field Ising model

We show that the three-dimensional Ising model coupled to a small random magnetic field is ordered at low temperatures. This means that the lower critical dimension,d _l for the theory isd _l 2, settling a long controversy on the subject. Our proof is based on an exact Renormalization Group (RG) analysis of the system. This analysis is carried out in the domain wall representation of the system and it is inspired by the scaling arguments of Imry and Ma. The RG acts in the space of Ising models and in the space of random field distributions, driving the former to zero temperature and the latter to zero variance.     

Phase transition in the Blume-Capel model with second neighbour interaction

A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction (J ₂ <0) and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis. Received: 3 November 1997 / Revised: 31 March 1998 / Accepted: 7 April 1998     

Percolation transition in an irreversible-surface reaction model

Monte Carlo simulation studies of percolation transition in a surface reaction model describing the oxidation of carbon mono-oxide on a catalytic surface are presented. The percolation transition for adsorbed oxygen atoms occurs below the poisoning transition where carbon mono-oxide completely covers the surface of the catalyst and takes place for an oxygen coverage of about 0.525 which is close to the percolation transition in an Ising lattice gas with nearest-neighbor attractive interactions. In several respects the oxygen clusters near the percolation threshold resemble those of the Ising lattice gas near its critical point.