Kinetic Phase Transition in A2 ＋ 2B2 → 2B2A Reaction System with Particle Diffusion

A lattice gas model is presented for the A2 ＋2B2 → 2B2A reaction system with particle diffusion in two dimensions. In the model, B2 dissociates in the random dimer-filling mechanism and A2 dissociates in the end-on dimer filling mechanism. A reactive window appears and the system exhibits a continuous phase transition from a reactive state to a ＂B ＋ vacancy＂ covered state with infinitely many absorbing states. When the diffusion of particle B is considered, there are only two absorbing states. It is found that the critical behavior of the continuous phase transition changes from the directed percolation （DP） class to the pair contact process with diffusion （PCPD） class.     

Hysteresis behavior and nonequilibrium phase transition in a one-dimensional evolutionary game model

We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exploiting a cooperator is small. Furthermore, if b is large enough, then the system exhibits two continuous phase transitions between two absorbing states and a coexistence state of cooperation and defection, respectively. The tri-critical point is roughly estimated. Moreover, it is found that the critical behavior of the continuous phase transition with an absorbing state is in the directed percolation universality class.     

Phase Transition of the Pair Contact Process Model in a Fragmented Network

We investigate the phase transition of the pair contact process （PCP） model in a fragmented network. The network is formed by rewiring the link between two nearest neighbors to another randomly selected site in one dimension with a probability q. When the average degree （k〉 = 2, the system exhibits a structure transition and the lattice is fragmented into several isolated subgraphs, it is shown that a giant cluster appears and its node fraction does not change nearly for q 〉 0. Furthermore, it is found that the critical behavior of the continuous phase transition for the PCP model is different from the directed percolation （DP） class and the estimated values of the critical exponents are independent of the rewiring probability for q 〉 0. We conjecture that the structure transition for （k） = 2 takes an important role in the change of the critical behavior of the continuous phase transition.     

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive (ferromagnetic interaction) and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative (ferromagnetic or anti-ferromagnetic interaction). The temperature dependence of the layer magnetizations of the system is examined to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the phase transition temperatures. The system exhibits both second-and first-order phase transitions besides triple point (T P ), critical end point (E), multicritical point (A), isolated critical point (C) and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in N′eel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.     

Criticality of Epidemic Spreading in Mobile Individuals Mediated by Environment

We investigate the critical behaviour of an epidemical model in a diffusive population mediated by a static vector environment on a 2D network. It is found that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. Finite-size and short-time dynamic scaling relations are used to determine the critical population density and the critical exponents characterizing the behaviour near the critical point. The results are compatible with the universality class of directed percolation coupled to a conserved diffusive field with equal diffusion constants.     

Phase transitions of two spin-1/2 Baxter–Wu layers coupled with Ising-type interactions

Using a Monte Carlo simulation and the single histogram reweighting technique,we study the critical behaviors and phase transitions of the Baxter-Wu(BW)model on a two-layer triangular lattice with Ising-type interlayer couplings.Via the finite-size analysis,we obtain the transition temperatures and critical exponents at repulsive and attractive interlayer couplings.The data for the repulsive interlayer coupling suggest continuous transitions,and the critical behaviors are the same as those of the 2D BW model,belonging to the four-state Potts universality class.The reduced energy cumulants and the histograms reveal that attractive coupling leads to weak firstorder phase transitions.The pseudocritical exponents with the existence of the interlayer couplings indicate that the first-order transition is very close to the critical point of the 2D standard BW model.     

Anisotropic Effects on Magnetoelastic Transition in Magnetic Molecular Rings

We numerically study the anisotropic effects on the magnetoelastic transition in an S = 1/2 XXZ model with a finite lattice number. It is found that the order of the magnetoelastic transition is strongly affected by the anisotropy parameter λ and there may exist a critical λe dividing the first-order transition and the continuous transition.     

Hyperchaos--chaos--Hyperchaos Transition in a Class of On--Off Intermittent Systems Driven by a Family of Generalized Lorenz Systems

Blowout bifurcation in nonlinear systems occurs when a chaotic attractor lying in some symmetric subspace becomes transversely unstable. A class of five-dimensional continuous autonomous systems is considered, in which a two-dimensional subsystem is driven by a family of generalized Lorenz systems. The systems have some common dynamical characters. As the coupling parameter changes, blowout bifurcations occur in these systems and brings on change of the systems＇ dynamics. After the bifurcation the phenomenon of on-off intermittency appears. It is observed that the systems undergo a symmetric hyperchaos-chaos-hyperchaos transition via or after blowout bifurcations. An example of the systems is given, in which the drive system is the Chen system. We investigate the dynamical behaviour before and after the blowout bifurcation in the systems and make an analysis of the transition process. It is shown that in such coupled chaotic continuous systems, blowout bifurcation leads to a transition from chaos to hyperchaos for the whole systems, which provides a route to hyperchaos.     

Criticality of Parasitic Disease Transmission in a Diffusive Population

Through using the methods of finite-size effect and short time dynamic scaling, we study the critical behavior of parasitic disease spreading process in a diffusive population mediated by a static vector environment. Through comprehensive analysis of parasitic disease spreading we find that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. We determine the critical population density, above which the system reaches an epidemic spreading stationary state. We also perform a scaling analysis to determine the order parameter and critical relaxation exponents. The results show that the model does not belong to the usual directed percolation universality class and is compatible with the class of directed percolation with diffusive and conserved fields.     

Entangled multi-knot lattice model of anyon current

We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyons. Long-range coupling interaction is a fundamental character of this knot lattice model. The short-range coupling models, such as the Ising model,Hamiltonian model of quantum Hall effect, fermion pairing model, Kitaev honeycomb lattice model, and so on, are the short-range coupling cases of this knot lattice model. The long-range coupling knot lattice model bears Abelian and nonAbelian anyons, and shows integral and fractional filling states like the quantum Hall system. The fusion rules of anyons are explicitly demonstrated by braiding crossing states. The eigenstates of quantum models can be represented by a multilayer link lattice pattern whose topology is characterized by the linking number. This topological linking number offers a new quantity to explain and predict physical phenomena in conventional quantum models. For example, a convection flow loop is introduced into the well-known Bardeen–Cooper–Schrieffer fermion pairing model to form a vortex dimer state that offers an explanation of the pseudogap state of unconventional superconductors, and predicts a fractionally filled vortex dimer state. The integrally and fractionally quantized Hall conductance in the conventional quantum Hall system has an exact correspondence with the linking number in this multi-knot lattice model. The real-space knot pattern in the topological insulator model has an equivalent correspondence with the Lissajous knot in momentum space. The quantum phase transition between different quantum states of the quantum spin model is also directly quantified by the change of topological linking number, which revealed the topological character of phase transition. Circularized photons in an optical fiber network are a promising physical implementation of this multi-knot lattice, and provide a different path to topological quantum computation.     

Phase Diagram of XY Model with Nematic Coupling on the Simple Cubic Lattice

Using cluster Monte Carlo method,we numerically investigate the criticality in the XY model with nematic coupling on the simple cubic lattice.We determine critical lines belong to the three-dimensional XY universality class in variable of θ(2θ) between the XY-ferromagnetic(nematic) and disordered states.Furthermore,the phase transition between the XY-ferromagnetic and the nematic states is found to be in the three-dimensional Ising universality class.The critical points are determined from the intersections of Binder ratios for various system sizes.With two sets of critical points obtained,we finally construct the phase diagram on the-J plane.     

QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation

The self-consistent mean field approximation of the two-flavor NJL model,with a free parameter a to reflect the competition between the "direct" channel and the "exchange" channel,is employed to study the QCD phase structure at finite iso spin chemical potential μ_I,finite bary on chemical potential μ_B and finite temperature T,and especially to study the location of the QCD critical point.Our results show that in order to match the corresponding lattice results of iso spin density and energy density,the contributions of the "exchange" channel need to be considered in the framework of the NJL model,and a weighting factor α=0.5 should be taken.It is also found that for fixed isospin chemical potentials,the lower temperature of the phase transition is obtained with increasing a in the T-μ_I plane,and the largest difference of the phase transition temperature with different a's appears at μ_I~1.5 mπ.At μ_I=0 the temperature of the QCD critical end point(CEP) decreases with increasing a,while the critical baryon chemical potential increases.At high isospin chemical potential(μ_I=500 MeV),the temperature of the QCD tricritical point(TCP) increases with increasing a,and in the low temperature regions the system will transition from the pion superfluidity phase to the normal phase as μ_B increases.At low density,the critical temperature of the QCD phase transition with different a's rapidly increases with μ_I at the beginning,and then increases smoothly around μ_I 300 MeV.In the high baryon density region,the increase of the iso spin chemical potential will raise the critical baryon chemical potential of the phase transition.     

Effect of the Coadsorption of CO and O2 on the Phase Diagram of the Ziff—Gulari—Barshad Model

The effect of the coadsorption of CO and O2 on the Ziff-Gulari-Barshad surface catalytic reaction system in studied by Monte Carlo simulation.The coadsorption of both species adds an extra reaction step to the classical Ziff-Gulari-Barshad model.It is shown that the second-order phase transition from the reactive state to the O-passivated state in the Ziff-Gulari-Barshad model is eliminated,and the production rate of CO2 increases linearly along the fraction yco of CO in gas phase when it is low,in agreement with experimental results.We also find that the increase of the probability of the coadsorption leads to the decrease of the critical value of yco of the discontinuous phase transition to the CO-passivated state.     

Decay of Loschmidt Echo at a Critical Point in the Lipkin-Meshkov-Glick model

An analytical expression of the Loschmidt echo in the Lipkin-Meshkov Gliek model is derived in the thermody- namical limit. It is used in the study of the decaying behaviour of the echo at the critical point of a quantum phase transition of the model It is shown that the echo has a power law decay for relatively long times.     

Quantum Tunneling of a Dipolar Bose-Einstein Condensate in Optical Lattice

We study quantum tunneling of a dipolar Bose-Einstein condensate in optical lattice when the spin system initially is prepared in a squeezed coherent state. It is found that there exists quantum tunneling between lattices l and l ＋ 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, quantum tunneling disappears between lattices l and l ＋ 1, and that l and l - 1. Correspondingly, the magnetic soliton appears.     

Magnetoelastic Instability in Ring-Shaped Molecule Magnets with Next-Nearest Neighbor Coupling

In considering next-nearest neighbor （NNN） coupling, we numerically investigate the magnetoelastic instability in ring-shaped mesoscopic antiferromagnetic Heisenberg spin 1/2 systems with spin-phonon interaction. The results indicate that, for antiferromagnetic NNN coupling J2, there may be a critical value J2^c, at which the ground state is dimerized for arbitrary lattice spring constant and beyond and below which the magnetoelastic instability behavior is different from each other. The values of J2^c are irrelevant to the system size. For ferromagnetic NNN coupling, only continuous transition is present from dimerized phase to uniform phase as lattice spring constant is increased.     

Mott transition in ruby lattice Hubbard model

Mott transition in a ruby lattice with fermions described by the Hubbard model including on-site repulsive interaction is investigated by combining the cellular dynamical mean-field theory and the continuous-time quantum Monte Carlo algorithm. The effect of temperature and on-site repulsive interaction on the metallic–insulating phase transition in ruby lattice with fermions is discussed based on the density of states and double occupancy. In addition, the magnetic property of each phase is discussed by defining certain magnetic order parameters. Our results show that the antiferromagnetic metal is found at the low temperature and weak interaction region and the antiferromagnetic insulating phase is found at the low temperature and strong interaction region. The paramagnetic metal appears in whole on-site repulsive interaction region when the temperature is higher than a certain value and the paramagnetic insulator appears at the middle scale of temperature and on-site repulsive interaction.     

Chaos in Einstein—Maxwell—Dust System

We study the dynamics of the Einstein-Maxwell-dust system and find that the system presents a critical point of a centre-centre-type structure in the phase space. By performing the numerical experiments, we find that the dynamics of the Einstein-Maxwell-dust system is unstable and its chaotic behaviour is obvious when the Hamiltonian becomes smaller.