Critical Relaxation of Stochastic lsing Model

Abstract

A markoffian stochastic model of interacting Ising spins is discussed near its critical point. The long time behavior of relaxation of its magnetization and energy is investigated near T_c by the use of high-temperature series expansion and the ratio method. The numerical estimate of the critical exponent Δ_MM of slowing down of magnetization is made, the results of which show Δ_MM\simeq2 for the simple square and triangular lattices, and Δ_MM\simeq1.4 for the simple cubic lattice. The exponent Δ_EE of slowing down of energy is also estimated, which gives the result Δ_EE\simeq2 for the simple square and triangular lattices. The method to derive high-temperature expansion of an n-spin correlation function ⟨σ₁σ₂…σ_n⟩ for an Ising model of spin 1/2 by the use of an equation of detailed balance is presented and applied to these estimates.