Higher-order calculations in the real space dynamic renormalization group: One dimension

The application of real space dynamic renormalization group methods to the one-dimensional kinetic Ising model, discussed in an earlier paper, is extended to one order higher in perturbation theory than was done previously. It is shown that the treatment of short-range, local quantities is improved in going to higher order in the perturbation expansion, while that of the long-range properties remains largely unaffected. Arbitrariness in the real space mapping function and how it may be exploited to our advantage is duscussed. It is shown that the renormalized Hamiltonian continues to be characterized by one coupling through second order. We find that the single spin-flip kinetic Ising model generates at second-order new spin-flip mechanisms in the renormalized dynamical operator but that their effects are small (at most 2%) over the entire temperature range.     

Majority-Vote Cellular Automata, Ising Dynamics, and P-Completeness

We study cellular automata where the state at each site is decided by a majority vote of the sites in its neighborhood. These are equivalent, for a restricted set of initial conditions, to nonzero probability transitions in single spin-flip dynamics of the Ising model at zero temperature. We show that in three or more dimensions these systems can simulate Boolean circuits of AND and OR gates, and are therefore P-complete. That is, predicting their state t time-steps in the future is at least as hard as any other problem that takes polynomial time on a serial computer. Therefore, unless a widely believed conjecture in computer science is false, it is impossible even with parallel computation to predict majority-vote cellular automata, or zero-temperature single spin-flip Ising dynamics, qualitatively faster than by explicit simulation.     

A mean-field equation of motion for the dynamic Ising model

A mean-field type of approximation is used to derive two differential equations, one approximately representing the average behavior of the Ising model with Glauber (spin-flip) stochastic dynamics, and the other doing the same for Kawasaki (spin-exchange) dynamics. The proposed new equations are compared with the Cahn-Allen and Cahn-Hilliard equations representing the same systems and with information about the exact behavior of the microscopic models.     

The kinetic Ising model: Exact susceptibilities of two simple examples

The susceptibility of a modified version of the one-dimensional kinetic Ising model is obtained and compared with the susceptibility of the Glauber version of this model. Spin-flip rates in the new model are picked so no spin-flip rate vanishes as the temperature vanishes. Despite the more rapid spin flips, the new model exhibits an infinitely slow approach to equilibrium in the low-temperature limit which is similar to the slowing down exhibited in the Glauber model. The new model also exhibits two different decay rates toward equilibrium, which are called the transient and slow decay rates. The Glauber model is characterized by only a single decay rate toward equilibrium.Work supported in part by National Science Foundation grant DMR 78-03408.     

Monte Carlo computer experiments on critical phenomena and metastable states

Ising and Heisenberg models are studied by the Monte Carlo method. Several hundred up to 60 000 spins located at two- and three-dimensional lattices are treated and various boundary conditions used to elucidate various aspects of phase transitions. Using free boundaries the finite size scaling theory is tested and surface properties are derived, while the periodic boundary condition or the effective field-like ‘self-consistent’ boundary condition are used to derive bulk critical properties. Since Monte Carlo averages can be interpreted as time averages of a stochastic model, ‘critical slowing down of convergence’ occurs. The critical dynamics is investigated in the case of the single spin-flip kinetic Ising model. Also non-equilibrium relaxation processes are treated, e.g. switching on small negative fields the magnetization reversal and nucleation processes are studied. The metastable states found can be understood in terms of a scaling theory and the droplet model. Using a spin exchange model the phase separation kinetics of a binary alloy is simulated.     

A microscopic derivation of the classical nucleation equation

The Becker-Döring equation of classical nucleation theory is derived in the framework of spin-flip dynamics of the Ising model. The derivation is based on a microscopic analysis of droplet geometry at low temperature.     

Magnetic properties and thermodynamics of decorated Ising chain with pendants of arbitrary spin

The decorated Ising chain with pendants of arbitrary spin and the single-ion anisotropy is exactly solved by the transfer matrix method. The solutions reveal abundant novel properties than the conventional one-dimensional Ising model. It is compared with the experimental data of a necklace-like molecule-based magnet, that gives a qualitative consistency.     

光电负反馈下垂直腔表面发射激光器偏振开关特性研究

基于扩展的自旋反转模型, 对光电负反馈下垂直腔表面发射激光器的偏振开关特性进行了数值仿真和理论分析. 研究结果表明: 对于不同的自旋反转率, 反馈强度和延迟时间对激光器偏振开关特性产生较大影响.在慢自旋反转率下运行时, 随着反馈强度的增加, 开关点电流呈线性增加, 导致X偏振模被压缩, 这与报道的基于各向同性光反馈的情景相反, 产生这一现象的原因是由于光电负反馈提高了X偏振模的阈值; 延迟时间对开关点电流的影响随反馈强度的变化而不同.在快自旋反转率下运行时, 反馈强度对开关点电流的影响与慢自旋反转率时的情形不同, 开关点电流经历先增加后减小的过程, 开关点电流受反馈强度的影响更加敏感; 而延迟时间的影响规律和慢自旋反转率时相似. 此外, 还发现自发辐射噪声对激光器偏振开关特性有较大影响. 关键词： 垂直腔表面发射激光器 偏振开关 光电负反馈 自发辐射噪声     

Dynamics of an Ising chain under local excitation: a scanning tunneling microscopy study of Si(100) dimer rows at 5 K

An extension of the classical Ising model to a situation including a source of spin-flip excitations localized on the scale of individual spins is considered. The scenario is realized by scanning tunneling microscopy of the Si(100) surface at low temperatures. Remarkable details, corresponding to the passage of phasons through the tunnel junction, are detected by the STM within the short span between two atoms comprising an individual Si dimer.     

Critical Behavior of Spatial Evolutionary Game with Altruistic to Spiteful Preferences on Two-Dimensional Lattices

Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents ν, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model.     

Field-induced magnetic phase transitions in the Yafet-Kittel model

The Yafet-Kittel model for a two-sublattice ferrimagnet with an antiferromagnetic exchange interaction in one of the sublattices was developed to describe magnetic-field-induced phase transitions in the isotropic and Ising cases. Depending on the relative values of the exchange parameters of the inter-sublattice interaction and the intra-sublattice interaction in the isotropic case, two types of magnetic phase diagrams with two types of second-order phase transitions are possible: to the noncollinear phase and to the spin-flip phase, and, in the Ising case, three types of magnetic phase diagrams with first-order phase transitions are possible. Fiz. Tverd. Tela (St. Petersburg) 41, 1797–1799 (October 1999)     

Pair correlation function for Ising spins with competing dynamics

An interacting Ising spin system on a lattice with the competing influence of spin-flip (Glauber) and spin-exchange (Kawasaki) dynamics is studied. The exact nonequilibrium steady-state solution of the pair correlation function in one dimension is derived and compared with the simulation data. The two-dimensional solution, under some Ansatz, is also discussed.     

A systematical improvement of the migdal recursion formula

We construct a new perturbative expansion whose zeroth-order approximation gives the Migdal-Kadanoff recursion equations. By this expansion it is therefore possible to improve systematically the Migdal-Kadanoff results. The first-order corrections are computed for the Ising and bond percolation models. The second-order corrections are computed only for the two-dimensional Ising model. Our method can be easily extended to other systems like the non-linear σ model or gauge theories.     

Interface motion in a planar spin-flip model derived from exclusion on the line

We consider a two-dimensional spin-flip model, which can be interpreted as the limit of the Ising model at low temperature and a small nonzero external field. In the hydrodynamic limit and for a special class of initial conditions, the motion of the interface is governed by a nonlinear partial differential equation with a lattice-distorted curvature term. In our proofs we use results about the hydrodynamic behavior of the weakly asymmetric exclusion process on the integers and also on the nonnegative integers with a trap at the boundary.     

Griffiths-McCoy singularities in random quantum spin chains: exact results through renormalization

The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singular quantities in the Griffiths phase of random quantum spin chains. For the random transverse-field Ising spin chain we have extended Fisher's analytical solution to the off-critical region and calculated the dynamical exponent exactly. Concerning other random chains we argue by scaling considerations that the RG method generally becomes asymptotically exact for large times, both at the critical point and in the whole Griffiths phase. This statement is checked via numerical calculations on the random Heisenberg and quantum Potts models by the density matrix renormalization group method.     

Spin-flip scattering of conduction electrons by dislocations in a metal

The spin-flip scattering of conduction electrons by dislocations in metals with a strong spin-orbit coupling is considered. Calculations are performed in terms of the model spin-orbit potential describing the spin-flip scattering of conduction electrons. It is shown that deformation of the crystal lattice in a metal leads to a change in the structure factor. The core of a rectilinear edge dislocation is calculated by the molecular dynamics method. The results obtained are compared with the experimental data on conduction-electron spin resonance (CESR) in copper.     

Chain length probability distribution — equivalence of ASYNNNI and 1d Ising model

An expression for the chain length probability distribution p(l) of a one dimensional Ising chain was derived using the cluster variation method formalism, the p(l) being expressed through the pair cluster probabilities. It was shown numerically that the same expression also applies in the case of one dimensional chains formed along one of the next-nearest neighbor interactions included in the two dimensional ASYNNNI (Asymmetric Next-Nearest Neighbor Ising) model, widely used to describe the statistics of oxygen ordering in the basal CuO _x planes of the YBa₂Cu₃O_6+x type high-T _c superconducting materials. Equivalency between ASYNNNI and 1d Ising model is discussed.      

Two-scale modeling of adsorption processes at structured surfaces

We present an algorithm for the simulation of vicinal surface growth. It combines a lattice gas anisotropic Ising model with a phase-field model. The molecular behavior of individual adatoms is described by the lattice gas model. The microstructure dynamics on the vicinal surface are calculated using the phase-field method. In this way, adsorption processes on two different length scales can be described: nucleation processes on the terraces (lattice gas model) and step-flow growth (phase field model). The hybrid algorithm that is proposed here, is therefore able to describe an epitaxial layer-by-layer growth controlled by temperature and by deposition rate. This method is faster than kinetic Monte Carlo simulations and can take into account the stochastic processes in a comparable way.     

On the thermodynamics of the random one-dimensional Ising chain in a transverse field

For three simple one-dimensional disordered models: (a) the Ising chain with random magnetic moments in a transverse field, (b) the Ising chain with random coupling constants in a transverse field, and (c) the X-Y model with a special type of disorder, the asymptotic equivalence in the thermodynamic limit is proved and some of its consequences are discussed. The spectral density of the finite chain for the model (a) is calculated by Dean's method for several representative cases and the presence of the local modes is indicated. The expressions for the initial susceptibilities for the models (a) and (b) are reviewed and (in two cases) the derivations are simplified.     

Decomposition of Ising spin of spin-S Ising model

We propose a general method by which an Ising spin of a spin-S Ising model is decomposed into Ising spins less than S. Some exactly solvable spin-S Ising models with S greater than 1/2 are obtained without using Horiguchi's condition or its extended conditions. These systems are reduced to the Ising model of spin ± 1 or an Ashkin-Teller model.