Relaxation of the Spin Autocorrelation Function in the Kinetic Ising Model with Bond Dilution

Abstract

The relaxation of the equilibrium correlation function q ( t )= N -1 Σ i =1 N is studied by the Monte Carlo method for the bond-diluted kinetic Ising model on the square lattice with a bond concentration below the percolation threshold. Here, the system has N Ising spins and S i denotes the i -th Ising spin. The correlation function q ( t ) seems to exhibit a nonexponential decay below the critical temperature of the nonrandom Ising model. An effective size ν of a cluster of ferromagnetically connected spins is defined as ν=(ln τ) 2 , where τ is the longest relaxation time in the cluster. It is found that the distribution function of ν behaves as P (ν)∝exp [-γν]. Although the asymptotic belaavior q ( t )∼exp [- C (ln t ) 2 ] is not reached in the time region studied by the Monte Carlo method, this distribution explains the long-time behavior of q ( t ).