Monte Carlo studies of the kinetic Ising model

Abstract

Results are presented for the computer simulation of the time-dependent behavior of the Ising model on a 100 × 100 lattice. Groups of particles are regarded as samples from an infinite lattice and the interactions between the sample particles and those outside are expressed through new boundary conditions based on extending the concept of mean field in a self-consistent way. These new boundary conditions are explored analytically for a few small samples and a sharp critical point is found in contrast to periodic boundary conditions. The relaxation times for long-range order and nearest-neighbor correlation (energy) for the 100 × 100 system have been computed and the corresponding critical exponents estimated. The results are ${\Delta }_{\delta \mu }=2.30\mathrm{}\pm 0.30$ and ${\Delta }_{\delta \mathcal{H}}=0.38\mathrm{}\pm 0.04$; these are compared with other recent results from computer simulations and series calculations.