Gaussian random field p-spin-interaction ising model in a transverse field

The Gaussian random field Ising model with p-spin interactions in the presence of a transverse field is studied by combining the Suzuki-Trotter approach and the thermodynamic perturbation theory. The first-order phase transitions are found in the limit p → ∞, in contrast to the cases with p=2.     

Monte Carlo technique for very large ising models

Rebbi's multispin coding technique is improved and applied to the kinetic Ising model with size 600*600*600. We give the central part of our computer program (for a CDC Cyber 76), which will be helpful also in a simulation of smaller systems, and describe the other tricks necessary to go to large lattices. The magnetizationM atT=1.4*T _c is found to decay asymptotically as exp(-t/2.90) ift is measured in Monte Carlo steps per spin, and M(t = 0) = 1 initially.     

Fast vectorized algorithm for the Monte Carlo simulation of the random field Ising model

An algorithm for the simulation of the 3-dimensional random field Ising model with a binary distribution of the random fields is presented. It uses multi-spin coding and simulates 64 physically different systems simultaneously. On one processor of a Cray YMP it reaches a speed of 184 million spin updates per second. For smaller field strength we present a version of the algorithm that can perform 242 million spin updates per second on the same machine.     

Calculation of a characteristic fractal dimension in the one-dimensional random field ising model

By exploiting the connection with the problem of a repeller in a one dimensional map a new method is applied to calculate a fractal dimension characterising the local field. It is determined analytically in powers of the strength of the random field and also by an iteration procedure.     

On the interface stiffness of the random field ising model

Recent results of Grinstein, Ma, Villain and Binder on interface roughening incontinuum andlattice random field Ising models are related by introducing an effective interface stiffness function {ei247-1}. Ford3 dimensions the continuum theory is shown to be valid for non-zero random field strengthh for all temperatures and on a length scaleL>l _d (h,T) _d (h,T). Ford=2 and smallT a smeared spin-glass transition occurs at ₂(h,T)h. It is argued, that for 3<d<5 interface roughening occurs only forh larger than a critical field strengthh _R (T).     

Localization in the ground state of the ising model with a random transverse field

We study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by $$H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} } $$ whereJ>0,x,y∈Z ^d, σ₁, σ₃ are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Z ^d} are independent identically distributed random variables. We consider the ground state correlation function 〈σ₃(x)σ₃(y)〉 and prove:

1. Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Z ^d, that $$\left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle \leqq C_{x,h} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _{x h} <∞.
2. Letd≧2. IfJ is sufficiently large, then, for almost every choice of the random transverse fieldh, the model exhibits long range order, i.e., $$\mathop {\overline {\lim } }\limits_{\left| y \right| \to \infty } \left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle > 0$$ for anyx∈Z ^d.

     

Two-dimensional ising models with competing interaction—a Monte Carlo study

Two-dimensional Ising models on a square lattice with competing interactions along one axis or both axes are studied primarily by the Monte Carlo method. Several commensurate-incommensurate transitions are found. Dislocation-like configurations are identified near the sinusoidal — paramagnetic transition in accordance with the idea that the transition might be of Kosterlitz-Thouless, XY-like character.     

Susceptibility and magnetisation of a random ising model

The susceptibility of a bond disordered Ising model is calculated by configurationally averaging an Ornstein-Zernike type of equation for the two spin correlation function. The equation for the correlation function is derived using a diagrammatic method due to Englert. The averaging is performed using bond CPA. The magnetisation is also calculated by averaging in a similar manner a linearised molecular field equation. Part of the work was done, while one of the authors (DK) was visiting International Centre for Theoretical Physics, Trieste, Italy.     

Correlation-length-exponent relation for the two-dimensional random ising model

We consider the two-dimensional (2D) random Ising model on a diagonal strip of the square lattice, where the bonds take two values, J1>J2, with equal probability. Using an iterative method, based on a successive application of the star-triangle transformation, we have determined at the bulk critical temperature the correlation length along the strip xi(L) for different widths of the strip L相似文献   

Monte Carlo evidence for inhomogeneous states in the two-dimensional classical Heisenberg model

It is emphasized that topologically classifiable, finite energy intrinsic defect states are known analytically for the continuum classical, isotropic, Heisenberg model in two space dimensions both from statistical mechanics and field theory literature. Evidence from Monte Carlo simulations is presented for the existence of these nonlinear, metastable states at low temperatures.     

蒙特卡罗模拟在非平衡动态系统中的应用

非平衡系统几乎存在于自然和人造系统的各个层面上,它以非零连续的流量为特征。完全非对称简单排他过程被认为是对这类系统建模和模拟的一个范例。对蒙特卡罗方法如何模拟该类系统进行了介绍。分析了通过蒙特卡罗模拟观察到的一些有趣的物理现象如自发性对称破缺、有限尺寸效应和跳跃过程。非对称的低-低密度相破缺与系统的有限尺寸效应密切相关,建议开展更细致的蒙特卡罗模拟以进一步加深对仍处于争论中的非平衡系统有限尺寸效应的认识。     

蒙特卡罗模拟在非平衡动态系统中的应用

非平衡系统几乎存在于自然和人造系统的各个层面上,它以非零连续的流量为特征。完全非对称简单排他过程被认为是对这类系统建模和模拟的一个范例。对蒙特卡罗方法如何模拟该类系统进行了介绍。分析了通过蒙特卡罗模拟观察到的一些有趣的物理现象如自发性对称破缺、有限尺寸效应和跳跃过程。非对称的低-低密度相破缺与系统的有限尺寸效应密切相关,建议开展更细致的蒙特卡罗模拟以进一步加深对仍处于争论中的非平衡系统有限尺寸效应的认识。     

Hierarchical Monte Carlo methods for fractal random fields

Two hierarchical Monte Carlo methods for the generation of self-similar fractal random fields are compared and contrasted. The first technique, successive random addition (SRA), is currently popular in the physics community. Despite the intuitive appeal of SRA, rigorous mathematical reasoning reveals that SRA cannot be consistent with any stationary power-law Gaussian random field for any Hurst exponent; furthermore, there is an inherent ratio of largest to smallest putative scaling constant necessarily exceeding a factor of 2 for a wide range of Hurst exponentsH, with 0.30<H<0.85. Thus, SRA is inconsistent with a stationary power-law fractal random field and would not be useful for problems that do not utilize additional spatial averaging of the velocity field. The second hierarchical method for fractal random fields has recently been introduced by two of the authors and relies on a suitable explicit multiwavelet expansion (MWE) with high-moment cancellation. This method is described briefly, including a demonstration that, unlike SRA, MWE is consistent with a stationary power-law random field over many decades of scaling and has low variance.     

Critical behaviour of the ising model in a transverse field

A theory for the critical behaviour of the Ising model in a transverse field is presented. The existence of a central component in the spectral density of the longitudinal spin relaxation function is shown to result self-consistently from decay into itself and energy-fluctuation diffusion mode. Estimates of the various quantities are made forT nearT _c , the damping is seen to be temperature dependent. Our theory is appropriate for the caseΓ ～J whereΓ andJ are the magnitudes of the transverse field and the exchange interaction between the spins respectively. Its relevance to neutron scattering data on Van Vleck paramagnets is discussed.     

Glassy phases in a layered ising model with random interlayer exchange

Thermodynamics of a layered Ising model with infinite-range ferromagnetic intralayer interaction and random nearest-neighbor interlayer coupling is considered. A detailed analysis of the model with vanishing average interlayer coupling is presented. The Gibbs free energy is found in the critical region, and the existence of many metastable states is demonstrated. Thermodynamic parameters of the system are found for periodic states. As the mean square interlayer coupling increases, the equilibrium state of the system undergoes an infinite sequence of first-order phase transitions, the number of magnetic planes and the distance between them change discontinuously, and so do both bulk magnetization and magnetic susceptibility.     

A Monte Carlo simulation of random surfaces

We use a previously proposed stochastic process and carry out Monte Carlo simulations for two models of random surfaces defined on hypercubic lattices. Tests are carried out in five dimensions. The critical coupling constants are estimated for both models. One of the models allows also results on its entropy.     

Monte Carlo simulations of a model for opinion formation

A model for opinion formation based on the Theory of Social Impact is presented and studied by means of numerical simulations. Individuals with two states of opinion are impacted due to social interactions with: i) members of the society, ii) a strong leader with a well-defined opinion and iii) the mass media that could either support or compete with the leader. Due to that competition, the average opinion of the social group exhibits phase-transition like behaviour between different states of opinion.     

Bloch electron in a magnetic field and the ising model

The spectral determinant det(H-varepsilonI) of the Azbel-Hofstadter Hamiltonian H is related to Onsager's partition function of the 2D Ising model for any value of magnetic flux Phi = 2piP/Q through an elementary cell, where P and Q are coprime integers. The band edges of H correspond to the critical temperature of the Ising model; the spectral determinant at these (and other points defined in a certain similar way) is independent of P. A connection of the mean of Lyapunov exponents to the asymptotic (large Q) bandwidth is indicated.