MULTISPIN CODING TECHNIQUE FOR NONEQUILIBRIUM REWEIGHTING

We present the multispin coding for the nonequilibrium reweighting method of the Monte Carlo simulation, that was developed by the present authors. As an illustration, we treat the driven diffusive lattice gas model. We use the multispin coding technique both for the spin update and for the calculation of the histogram of incremental weights, which is needed in the calculation of nonequilibrium reweighting. All the operations are executed by the bitwise logical commands.

ISING MODEL AS TEST FOR SIMPLE RANDOM NUMBER GENERATORS

Monte Carlo simulations with up to 1765 spins show no significant deviations between four different random number generators in multispin coding, as opposed to multiplication with 16807 for one-word-per-spin coding for 325. Also world record sizes 10001922, 99843, 8804 and 486 spins were simulated.

MULTI-SPIN CODING OF THE MONTE CARLO SIMULATION OF THE THREE-STATE RANDOM POTTS MODEL AND THE BLOCK-SPIN TRANSFORMATION

The multi-spin coding of the Monte Carlo simulation of the three-state Potts model on the simple cubic lattice is presented. The ferromagnetic (F) model, the antiferromagnetic (AF) model, and the random mixture of the F and AF couplings are treated. The multispin coding technique is also applied to the block-spin transformation. The block-spin transformation of the F Potts model is simply realized by the majority rule, whereas the AF three-state Potts model is transformed to the block spin having a six-fold symmetry.

PHASE TRANSITION IN THREE-DIMENSIONAL ISING SYSTEMS WITH QUENCHED NON-MAGNETIC IMPURITIES: A REVIEW OF MONTE CARLO STUDIES

A review is given of Monte Carlo simulations for the phase transition in simple cubic Ising ferro-, ferri-, and antiferromagnets with quenched non-magnetic impurities of concentration x. Special emphasis is given on the description of a fully vectorized multispin coding program and on the problems related to the analysis of the Monte Carlo data. The following three subjects are discussed: 1) For ferro- and antiferromagnets, the critical behaviour of the order parameter is different from the one of the corresponding pure system, in agreement with the prediction of the Harris criterion. The possibly effective exponent β depends on x, whereas for ferrimagnets no such concentration dependence is revealed by the present study for x=0, 0.1, and 0.2.2) For strongly diluted systems, there is a maximum for the Kouvel-Fisher exponent γ(T) of the order-parameter susceptibility outside the critical regime, in accordance with the predictions of the correlated molecular field theory. 3) For the diluted antiferromagnet (x=0.5), a cusp emerges at T c for the uniform susceptibility, in agreement with the theory of Fishman and Aharony.