Classical Behavior After a Phase Transition: I. Classical Order Parameters

We analyze the onset of classical field configurations after a phase transition. Firstly, we motivate the problem by means of a toy model in quantum mechanics. Subsequently, we consider a scalar field theory in which the system-field interacts with its environment, represented both by further scalar fields and by its own short-wavelength modes. We show that for very rapid quenches, the order parameter can be treated classically by the time taken for it to achieve its ground state values (spinodal time).     

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.     

Classical Behavior After a Phase Transition: II. The Formation of Classical Defects

Classical defects (monopoles, vortices, etc.) are a characteristic consequence of many phase transitions of quantum fields. Most likely these include transitions in the early universe and such defects would be expected to be present in the universe today. We continue our analysis of the onset of classical behavior after a second-order phase transition in quantum field theory and show how defects appear after such transitions.     

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.     

自发磁化渗流模型的可视化演示实验

经过多年的发展,统计物理对自发磁化进行了深入研究并取得丰硕成果。但是对该理论,很多学生难以建立相应物理图像。借助自发磁化的渗流模型和Java语言,我们将自发磁化过程中铁磁物质磁性有无与系统微观形貌上所定义集团连通与否这一定量关系动态直观地展示给学生,从而达到增加感性认识,提高教学效果的目的。     

Existence of enantiomeric phase separation in a three-dimensional lattice gas model

A three-dimensional lattice gas model for enantiomeric phase separation is introduced. The enantiomeric molecules (d andl) are the two nonsuperimposable mirror images having the molecular structure C(AB)₂, where C is a tetrahedrally bonded carbon atom with one bond to each end of two AB groups. The lattice gas model consists of a body-centered cubic lattice, each site of which can be either vacant or occupied by a molecule oriented so that the A and B groups point toward neighboring lattice sites. Pairs of molecules interact with short-range, orientationally-dependent interactions. For a domain of interaction parameters, the Pirogov-Sinai extension of the Peierls argument is used to prove thatd-rich andl-rich phases exist in the model at sufficiently low temperature. For another domain of interaction parameters, at sufficiently high chemical potential there is an infinite number of ground states, each containing a racemic mixture ofd andl molecules.     

Characteristics of phase transitions via intervention in random networks

We present a percolation process in which the classical Erdo¨s–Re′nyi(ER) random evolutionary network is intervened by the product rule(PR) from some moment t0. The parameter t0is continuously tunable over the real interval [0, 1].This model becomes the random network under the Achlioptas process at t0= 0 and the ER network at t0= 1. For the percolation process at t0≤ 1, we introduce a relatively slow-growing point, after which the largest cluster begins growing faster than that in the ER model. A weakly discontinuous transition is generated in the percolation process at t0≤ 0.5.We take the relatively slow-growing point as the lower pseudotransition point and the maximum gap point of the order parameter as the upper pseudotransition point. The critical point can be approximately predicted by each fitting function of the two points about t0. This contributes to understanding the rapid mergence of the large clusters at the critical point.The numerical simulations indicate that the lower pseudotransition point and the upper pseudotransition point are equal in the thermodynamic limit. When t0> 0.5, the percolation processes generate a continuous transition. The scaling analyses of several quantities are presented, including the relatively slow-growing point, the duration of the relatively slow-growing process, as well as the relatively maximum strength between the percolation percolation at t0< 1 and the ER network about different t0. The presented mechanism can be viewed as a two-stage percolation process that has many potential applications in the growth processes of real networks.     

Existence of several surface-reconstructed phases in a two-dimensional lattice model

The zero-temperature phase diagram is rigorously obtained for a two-dimensional lattice model with four energy parameters. It is shown that the parameter space can be divided into regions, together with their boundaries, such that in each region the ground-state configurations are of one of seven different types. These types include one which is nondegenerate, four which are doubly degenerate, one which is infinitely degenerate but with no residual entropy, and one which is infinitely degenerate and has a nonzero residual entropy. The Pirogov-Sinai extension of the Peierls argument is used to establish the existence at low temperatures of four different types of ordered surface-reconstructed phases.     

Steered Quantum Coherence as a Signature of Topological Quantum Phase Transitions in the Extended XY Model

In recent years, there has been a surge of interest in exploring coherence measures and correlation measures to characterize topological quantum phase transitions (TQPTs). Here, motivated by the continued push in this direction, the steered quantum coherence (SQC) in the extended XY model is studied to analyze its capability in characterizing TQPTs. It is shown that the first derivative of SQC succeeds in signaling different critical points of TQPTs. In particular, it is found that the SQC is a long-range correlation and the first derivative of SQC can always accurately identify TQPTs for different site distance.     

Sharpness of the Phase Transition and Exponential Decay of the Subcritical Cluster Size for Percolation on Quasi-Transitive Graphs

We study homogeneous, independent percolation on general quasi-transitive graphs. We prove that in the disorder regime where all clusters are finite almost surely, in fact the expectation of the cluster size is finite. This extends a well-known theorem by Menshikov and Aizenman & Barsky to all quasi-transitive graphs. Moreover we deduce that in this disorder regime the cluster size distribution decays exponentially, extending a result of Aizenman & Newman. Our results apply to both edge and site percolation, as well as long range (edge) percolation. The proof is based on a modification of the Aizenman & Barsky method.     

Percolation Thresholds in Ternary Polymer Melt Blends with Separate Dispersions of the Inner Phases: Mathematical Model

A mathematical model based on a straightforward geometrical background is developed which enables predictions of a transition of one dispersed phase to a cocontinuous one (i.e., the percolation threshold) on addition of another dispersed phase during melt mixing in ternary polymer blends. The present work concerns only ternary blends with two separate dispersions of the inner phases in which no encapsulation takes place. In addition, in order to simplify the model, one of the inner phases was represented by hard, nondeformable microspheres The expression developed describes well an experimental relationship between the percolation threshold, the concentration above which the former dispersed phase transforms to a continuous one, and concentrations of both inner phases. The results agree well with the experimental data obtained in a previous work.     

Topological Phase Transition and Phase Diagrams in a Two-Leg Kitaev Ladder System

A scheme to investigate the topological properties in a two-leg Kitaev ladder system composed of two Kitaev chains is proposed. In the case of two identical Kitaev chains, it is found that the interchain hopping amplitude plays a significant role in the separation of the energy spectrum and in inducing a topologically nontrivial phase, while the interchain pairing strength only affects the size of the energy gap. Moreover, another situation that the system consists of two non-identical Kitaev chains is also investigated and the corresponding phase diagram is calculated. It is found that two pairs of degenerate nonzero edge modes will, respectively, appear in the upper and lower energy gaps when the interchain hopping amplitude or the interchain pairing strength is large enough. Furthermore, it is pointed out that the winding number is quantitatively equivalent to half of the number of zero energy edge modes in our system.     

Percolation in hard-core lattice gases and a model ferrofluid

A lattice gas on ³ consisting of hard spheres with exclusions extending through third neighbors is proved to undergo a percolation transition. If spins with ferromagnetic couplings are attached to the spheres, spontaneous magnetization is proved to occur. This may provide a model for a ferrofluid, a system which exhibits spontaneous magnetization without crystalline order. Similar results are also obtained for an analogous model on ².     

Entanglement and quantum phase transition in a mixed-spin Heisenberg chain with single-ion anisotropy

We study the ground-state and thermal entanglement in the mixed-spin (S,s)=(1,1/2) Heisenberg chain with single-ion anisotropy D using exact diagonalization of small clusters. In this system, a quantum phase transition is revealed to occur at the value D=0, which is the bifurcation point for the global ground state; that is, when the single-ion anisotropy energy is positive, the ground state is unique, whereas when it is negative, the ground state becomes doubly degenerate and the system has the ferrimagnetic long-range order. Using the negativity as a measure of entanglement, we find that a pronounced dip in this quantity, taking place just at the bifurcation point, serves to signal the quantum phase transition. Moreover, we show that the single-ion anisotropy helps to improve the characteristic temperatures above which the quantum behavior disappears.     

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     

Dynamic Dipole and Quadrupole Phase Transitions in the Kinetic Spin-3/2 Model

The dynamic phase transition has been studied, within a mean-field approach, in the kinetic spin-3/2 Ising model Hamiltonian with arbitrary bilinear and biquadratic pair interactions in the presence of a time dependent oscillating magnetic field by using the Glauber-type stochastic dynamics. The nature (first- or second-order) of the transition is characterized by investigating the behavior of the thermal variation of the dynamic order parameters and as well as by using the Liapunov exponents. The dynamic phase transitions (DPTs) are obtained and the phase diagrams are constructed in the temperature and magnetic field amplitude plane and found nine fundamental types of phase diagrams. Phase diagrams exhibit one, two or three dynamic tricritical points, and besides a disordered (D) and the ferromagnetic-3/2 (F_3/2) phases, six coexistence phase regions, namely F _3/2+ F _1/2, F _3/2+ D, F _3/2+ F _1/2+ FQ, F _3/2+ FQ, F _3/2+ FQ + D and FQ + D, exist in which depending on the biquadratic interaction. PACS number(s): 05.50.+q, 05.70.Fh, 64.60.Ht, 75.10.Hk     

Effects of Bond Alternation on the Ground-State Phase Diagram of One-Dimensional XXZ Model

The ground-state properties and quantum phase transitions (QPTs) of the one-dimensional bond-alternative XXZ model are investigated by the infinite time-evolving block decimation (iTEBD) method.The bond-alternative effects on its ground-state phase diagram are discussed in detail.Once the bond alternation is taken into account,the antiferromagnetic phase (Δ 1) will be destroyed at a given critical point and change into a disordered phase without nonlocal string order.The QPT is shown to be second-order,and the whole phase diagram is provided.For the ferromagnetic phase region (Δ-1),the critical point r c always equals 1 (independent of Δ),and the QPT for this case is shown to be first-order.The dimerized Heisenberg model is also discussed,and two disordered phases can be distinguished by with or without nonlocal string orders.Both the bipartite entanglement and the fidelity per site,as two kinds of model-independent measures,are capable of describing all the QPTs in such a quantum model.