A history-dependent stochastic predator-prey model: Chaos and its elimination

A non-Markovian stochastic predator-prey model is introduced in which the prey are immobile plants and predators are diffusing herbivors. The model is studied by both mean-field approximation (MFA) and computer simulations. The MFA results a series of bifurcations in the phase space of mean predator and prey densities, leading to a chaotic phase. Because of emerging correlations between the two species distributions, the interaction rate alters and if it is chosen to be the value which is obtained from the simulation, then the chaotic phase disappears. Received 12 July 1999     

Mixed spin transverse Ising model with longitudinal random crystal field interactions

The effect of a longitudinal random crystal field interaction on the phase diagrams of the mixed spin transverse Ising model consisting of spin-1/2 and spin-1 is investigated within the finite cluster approximation based on a single-site cluster theory. In order to expand a cluster identity of spin-1, we transform the spin-1 to spin-1/2 representation containing Pauli operators. We derive the state equations applicable to structures with arbitrary coordination number N. The phase diagrams obtained in the case of a honeycomb lattice (N=3) and a simple-cubic lattice (N=6), are qualitatively different and examined in detail. We find that both systems exhibit a variety of interesting features resulting from the fluctuation of the crystal field interactions. Received: 13 February 1998 / Accepted: 17 March 1998     

Magnetic fluids in an external field

Within mean field approximation we investigate the phase diagrams of magnetic fluids in presence of a magnetic field. In a finite field the magnetic phase transition is absent, but instead a line of first order liquid-liquid transitions ending in a critical point occurs for a magnetic interaction, which is sufficiently strong. Varying the magnetic field these critical points extend from the tricritical point at H=0 to a critical endpoint. For a fluid with Ising spins we calculate the critical lines and several tricritical exponents analytically. For Heisenberg fluids we obtain the phase diagrams from a numerical solution of the mean field equations of state. Received 20 March 1998     

Finite cluster approximation for bond and site dilution transverse ising model on square lattice

The critical behaviour of the bond and site dilution transverse Ising model on a square lattice with spin-1/2 is investigated within the framework of the finite cluster approximation (FCA). The phase diagrams, critical temperature, critical transverse field and percolation threshold are given. The FCA method is conceptually as simple as an ordinary mean field approximation (MFA) but gives much better results.     

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     

Mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice within the effective-field theory

An effective-field theory with correlations is developed for a mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice. Spin-1 atoms and spin-3/2 atoms are distributed in alternative layers of a honeycomb lattice. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the interaction between the vertically aligned spins and adjacent spins are coupled either ferromagnetically or antiferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the temperature dependence of the total magnetization to find the compensation points and to determine the type of compensation behavior. We present the phase diagrams in different planes for h=0, and the phase diagrams contain the paramagnetic, nonmagnetic and ferrimagnetic phases. The system also presents a tricritical behavior besides multicritical point (A), isolated critical point (C) and double critical end point (B) depending on the interaction parameters.     

Interplay of the Staggered and Three-Body Interaction Potentials on the Quantum Phases of a Spin-1 Ultracold Atom in an Optical Lattice

The interplay of the staggered and the three-body interaction potentials on the quantum phases of a spin-1 Bose Hubbard model using a mean field approximation (MFA) is studied. In the antiferromagnetic (AF) case, a smaller value of the staggered potential (SP) results in the charge and the spin density wave ordering along with the Mott insulator (MI) and the staggered superfluid (SSF) phases. While the competition between two types of the potential leads to the stabilization of the higher order MI and charge density wave (CDW) phases with increasing three-body interaction strength. Further, the spin eigenvalue and nematic order parameters are calculated to scrutinize the spin singlet-nematic formation in the MI and the CDW phases and spin population fractions to analyze the nature of the SSF phase. A signature of the spin density wave (SDW) pattern is also observed in the gapped phase lobes. In case of a purely three-body interaction, the third and higher order insulating lobes become dominant with increasing staggered potential strength. Subsequently, all MFA phase diagrams are then nicely corroborated with the analytical results obtained using a perturbative expansion corresponding to the AF and ferromagnetic cases.     

Critical exponents of random XX and XY chains: Exact results via random walks

We study random XY and (dimerized) XX spin-1/2 quantum spin chains at their quantum phase transition driven by the anisotropy and dimerization, respectively. Using exact expressions for magnetization, correlation functions and energy gap, obtained by the free fermion technique, the critical and off-critical (Griffiths-McCoy) singularities are related to persistence properties of random walks. In this way we determine exactly the decay exponents for surface and bulk transverse and longitudinal correlations, correlation length exponent and dynamical exponent. Received 26 September 1999     

Thermal and magnetic properties of a ferrimagnetic nanoparticle with spin-3/2 core and spin-1 shell structure

Intensive Monte Carlo simulations based on standard Metropolis algorithm have been applied to investigate the phase diagrams of a ferrimagnetic cubic nanoparticle (nanocube) with a spin-3/2 core surrounded by a spin-1 shell layer with antiferromagnetic interface coupling. It has been shown that occupation of sites of particle core by spin-3/2 plays an important role on the shape of the phase diagrams. In addition, effects of the crystal field interaction as well as exchange interactions on the thermal and magnetic properties of the system have also been discussed in detail, and some interesting features have been observed for the temperature dependence of total magnetization curves of particle.     

一维自旋1键交替XXZ链中的量子纠缠和临界指数

利用基于张量网络表示的矩阵乘积态算法以及无限虚时间演化块抽取方法,本文研究了一维无限格点自旋1的键交替反铁磁XXZ海森伯模型中的量子相变.分别计算了系统的von Neumann熵、单位格点保真度和序参量,从而得到了系统随键交替强度的变化从拓扑有序Néel相到局域有序二聚化相的量子相变点.我们用矩阵乘积态方法拟合出了相变的中心荷c?0.5,表明此相变属于二维经典的Ising普适类.另外,通过对拓扑Néel序的数值拟合,我们得到了相变点处的特征临界指数β′=0.236和γ′=0.838.     

Ferromagnetic ordering in graphs with arbitrary degree distribution

We present a detailed study of the phase diagram of the Ising model in random graphs with arbitrary degree distribution. By using the replica method we compute exactly the value of the critical temperature and the associated critical exponents as a function of the moments of the degree distribution. Two regimes of the degree distribution are of particular interest. In the case of a divergent second moment, the system is ferromagnetic at all temperatures. In the case of a finite second moment and a divergent fourth moment, there is a ferromagnetic transition characterized by non-trivial critical exponents. Finally, if the fourth moment is finite we recover the mean field exponents. These results are analyzed in detail for power-law distributed random graphs. Received 4 April 2002 Published online 19 July 2002     

Mixed Ising system designed with integer and half-integer spins: dynamic behaviors under oscillating magnetic field

By using the simplified effective-field theory based on Glauber-type stochastic dynamics, namely the dynamic simplified effective-field theory, the dynamic phase diagrams of a two-dimensional mixed spin-1 and spin-3/2 Blume–Capel model are studied in an oscillating external magnetic field. The dynamic equations are derived for two interpenetrating square lattices. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are examined, and the dynamic phase diagrams are presented in the two different planes. The dynamic phase diagrams illustrate several ordered phases, the coexistence phase region and critical points as well as a re-entrant behavior depending on the interaction parameters. Finally, the discussion and comparison of the dynamic phase diagrams are given briefly.     

Phase diagrams of Ising films with competing interactions

The axial next-nearest-neighbour Ising (ANNNI) model of finite thickness is studied. Using mean-field theory, Monte Carlo simulations, and low-temperature analyses, phase diagrams are determined, with a distinct phase diagram for each film thickness. The robustness of the phase diagrams against varying the couplings in the surface layers is analysed. Received 19 March 2002 and Received in final form 2 April 2002 Published online 6 June 2002     

Phase diagrams of spin-1 Ising model with bilinear and quadrupolar interactions under magnetic field. Two-particle cluster approximation

The spin-1 Ising model with bilinear and quadrupolar short-range interactions under magnetic field is investigated within the two-particle cluster approximation. It is shown that for those values of the quadrupolar interaction when at zero magnetic field the system undergoes a temperature phase transition between quadrupolar and paramagnetic phases, a triple point may exist in the temperature vs. magnetic field phase diagrams, necessarily along with a critical point. It is also shown that the critical points in the temperature vs. magnetic field phase diagrams of the investigated model can be of three types.     

Ising-type critical exponents of the fully frustrated spin-1/2 Heisenberg FM/AF square bilayer at a critical magnetic field

The fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.     

The Glauber dynamics for a spin-1 metamagnetic Ising system with bilinear and biquadratic interactions

We present a study, within a mean-field approximation, of the dynamics of a spin-1 metamagnetic Ising system with bilinear and biquadratic interactions in the presence of a time-dependent oscillating external magnetic field. First, we employ the Glauber transition rates to construct the set of mean-field dynamic equations. Then, we study the time variation of the average order parameters to find the phases in the system. We also investigate the thermal behavior of dynamic order parameters to characterize the nature (first- or second-order) of the dynamic transitions. The dynamic phase transitions are obtained and the phase diagrams are constructed in two different the planes. The phase diagrams contain a disordered and ordered phases, and four different mixed phases that strongly depend on interaction parameters. Phase diagrams also display one or two dynamic tricritical points, a dynamic double critical end and dynamic quadruple points. A comparison is made with the results of the other metamagnetic Ising systems.     

Renormalization Group Study of the Mixed Spin-1 and Spin-3/2 Blume-Emery-Griffiths Model with Attractive Biquadratic Coupling

The mixed spin-1 and spin-3/2 Blume-Emery-Griffiths model with attractive biquadratic coupling is investigated in the framework of the Migdal-Kadanoff Renormalization Group method. By changing the ratio R > 0 of biquadratic and bilinear exchange interactions and according to the different values of crystal field interactions, we have determined six main types of phase diagrams. The full flow in the parameters space of the Hamiltonian was established and the fixed points obtained are drawn up in a table. In addition, we have determined the eigenvalues of the transformation of the group in the vicinity of the critical points. Finally, the introduction of a positive biquadratic interaction was discussed.

     

The kinetic spin-1 Blume-Capel model with competing dynamics

We have studied by means of Monte-Carlo simulation and exact finite-size analysis, the spin-1 Blume Capel model with Glauber and Kawasaki dynamics. The Kawasaki spin-exchange process transfers energy into the system from an external source. Some phase diagrams of the model are presented. For some parameter values, the system displays a kind of self-organization phenomenon within the disordered phase. Received 15 February 2000     

Ground-state magnetic properties of the spin-2 transverse Ising model

The ground-state magnetic properties of the spin-2 transverse Ising model with a longitudinal crystal field are studied within the framework of mean-field theory (MFT) and effective-field theory (EFT), respectively. The phase diagrams and magnetization curves are examined in detail. It is found that the system exhibits a tricritical behavior in the ground-state phase diagrams. Some interesting phenomena have been found, especially the first-order phase transition from one ordered phase to the other ordered phase, which is due to the high spin. The spin correlation has important effect on the magnetic properties of the system. We also find that the ground-state phase diagrams of the spin-2 transverse Ising model are very different from those of the spin-3/2 transverse Ising model.     

Phase diagrams of a nonequilibrium mixed spin-1/2 and spin-2 Ising ferrimagnetic system under a time-dependent oscillating magnetic field

We present phase diagrams for a nonequilibrium mixed spin-1/2 and spin-2 Ising ferrimagnetic system on a square lattice in the presence of a time dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The dynamic phase transition points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain paramagnetic (p) and ferrimagnetic (i) phases, and one coexistence or mixed phase region, namely the i+p, that strongly depend on interaction parameters. The system exhibits the dynamic tricritical point and the reentrant behaviors.