Phase Transition in a Generalized Eden Growth Model on a Tree

We study analytically the late time statistics of the number of particles in an Eden growth model on a tree. In this model, a cluster grows in continuous time on a binary Cayley tree, starting from the root, by absorbing new particles at the empty perimeter sites at a rate proportional to c ^−l where c is a positive parameter and l is the distance of the perimeter site from the root. For c=1, this model corresponds to random binary search trees and for c=2 it corresponds to digital search trees in computer science. By introducing a backward Fokker-Planck approach, we calculate the mean and the variance of the number of particles at large times and show that the variance undergoes a ‘phase transition’ at a critical value . While for the variance is proportional to the mean and the distribution is normal, for the variance is anomalously large and the distribution is non-Gaussian due to the appearance of extreme fluctuations. The model is generalized to one where growth occurs on a tree with m branches and, in this more general case, we show that the critical point occurs at .     

New Monte Carlo Simulations to a Generalized XY Model

A new combination Monte Carlo （MC） technique of the classical Metropolis algorithm and the Swendsen Wang cluster algorithm is proposed. Upon application of the MC technique, the thermodynamic properties of a generalized two-dimensional XY model with chiral Dzyaloshinski-Moriya （DM） interactions are simulated for various DM interactions. The specific heat, order parameter and the integrated correlation time are simulated, We find that there exists a high-temperature Kosterlitz-Thouless-type phase transition related to strong DM spin ehiralities. As the DM strength increases the critical temperature of the Kosterlitz-Thouless phase transition increases, It is shown that the combination algorithm is faster than the Metropolis algorithms.     

On the Singularity of the Free Energy at a First Order Phase Transition

At first order phase transition the free energy does not have an analytic continuation in the thermodynamical variable, which is conjugate to an order parameter for the transition. This result is proved at low temperature for lattice models with finite range interaction and two periodic ground-states, under the only condition that they satisfy the Peierls condition.Supported by Fonds National Suisse de la Recherche Scientifique.     

A Model with Simultaneous First and Second Order Phase Transitions

We introduce a two dimensional nonlinear XY model with a second order phase transition driven by spin waves, together with a first order phase transition in the bond variables between two “bond ordered phases”, one with local ferromagnetic order and another with local anti-ferromagnetic order. We also prove that at the transition temperature the bond-ordered phases coexist with a disordered phase as predicted by Domany, Schick and Swendsen [1]. This last result generalizes the result of van Enter and Shlosman [2] We argue that these phenomena are quite general and should occur for a large class of potentials. PACS number: 64.60.Cn, 75.10.Hk     

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 and Critical Behavior for XY Model on 2-Dimensional Random Triangle Lattice

The Monte Carlo renormalization group method is applied to discussing the nature of phase transition of XY model on 2-dimensional random triangle lattices. A line of fixed point and un-universal phase transition are found. The results are in agreement with Kosterlitz-Thouless theory. The susceptibility ehows a clear size-dependent behaviorin low temperature region. This means that it should be divergent in this region.     

Existence of a Phase Transition in a Continuous Quantum System

We prove the existence of a phase transition in the quantum Widom–Rowlison model in two dimension. The case of Boltzmann and Bose statistics are explicitly discussed.     

Berezinskii-Kosterlitz-Thouless Transition in a Two-Dimensional Random-Bond XY Model on a Square Lattice

We perform Monte Carlo simulations to study the two dimensional random-bond XY model on a square lattice. Two kinds of bond randomness with the coupling coefficient obeying the Gaussian or uniform distribution are discussed. It is shown that the two kinds of disorders lead to similar thermodynamic behaviors if their variances take the same value. This result implies that the variance can be chosen as a characteristic parameter to evaluate the strength of the randomness. In addition, the Berezinskii-Kosterlitz-Thouless transition temperature decreases as the variance increases and the transition can even be destroyed as long as the disorder is strong enough.     

Effect of Droplet Size on the First Order Ziff-Gulari-Barshad (ZGB) Phase Transition

We introduce a new method to analyze the coexistence region of the constant rate ensemble ZGB discontinuous transition. The method clearly delineates the spinodal and coexistence points in the constant rate ZGB model. Increase in system size reduces the gap between the spinodal and coexistence points. Next we quantify the effect of metastability by introducing a droplet/nucleus of CO occupied sites in the initial system. In systems with initial nucleus of increasing size the distance between the spinodal and the coexistence point decreases, until for a large enough droplet spanning the initial system, the spinodal and the coexistence points become indistinguishable.     

Geometric Phase in a Generalized Time-Dependent Karassiov-Klimov Model

By using of the invariant theory, we have studied the generalized time-dependent Karassiov-Klimov model, the dynamical and geometric phases are given, respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.     

Geometric Phase in a Generalized Time-Dependent Jaynes-Cummings Model

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent Jaynes-Cummings model. It is found that the geometric phases in a cycle case have nothing to do with the frequency of the electromagnetic wave, the energy difference between two levels of the atom, and the coupling strength between the atom and the light field.     

Dynamical Phase Transitions in the Disordered Two-Dimensional XY Model

We study the time evolution of the distance between two configurations of the site-disordered two-dimensional (2D) XY model submitted to metropolis dynamics on a square lattice. For concentrations between p = 0.6 and p = 0.9 (p_c = 0.59), dynamical transitions and three temperature regimes, similar to the case of pure 2D XY model, are found.     

Ferroelectric Phase Transition of first Order in BaTiO3

A microscopic model of BaTiO₃ is treated to describe static phenomena near the ferroelectric phase transition. In addition to the polarization, changes of the lattice constant at fixed pressure are also considered. That leads to a new explanation of the first order character of the transition, which is carried out not only qualitatively but also quantitatively. We investigate the dependence on pressure and external field. Agreement with the experiment through the adjustment of the parameters of the theory is obtained.     

临界点二级相变的有限时间热力学逼近

应用内可逆卡诺循环的方法,导出了各种物质在临界点附近可逆与不可逆二级相变普遍适用的比热跃变公式以及广义的受伦菲斯特方程。对简单（P,V,T）系统、超导、电介质顺电一铁电二级相变进行了应用讨论。     

Geometric Phase in a Generalized Time-Dependent Double-Boson Interaction Model

By using of the invariant theory and the large quantum numbers approximation, we have studied a generalized time-dependent double-Boson interaction model, the dynamical and geometric phases are given, respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.     

A Trial of Variational-Cumulant Expansion on Simple Ising Model With Second Order Phase Transition

The standard variational-cumulant expansion (VC) combined with a scheme for the enumeration of connected diagrams is employed to study the simple Ising model with the second-order phase transition. This model is evaluated to the 5th order approximations. A comparison with the 2-dimensional exact results shows that thermodynamic quantities converge rather slowly to the exact values in the intermediate region. A strict analytical calculation of the critical temperature with the 5th order approxinlation both for J_i and cumulant expansion suggests that VC chn achieve rather high standard accuracy if the variational parameters J_i could be determined up to higher degrees of corrections rather than the first one. Anomalies are found for U, C and M at extremely low temperature. A detailed study of M implies that thermodynamic formulae should be carefully chosen in VC approach so as to avoid these anomalies.