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

The relaxation of the equilibrium correlation function [formula omitted] 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 Sⁱ 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 v of a cluster of ferromagnetically connected spins is defined as [formula omitted], where τ is the longest relaxation time in the cluster. It is found that the distribution function of v behaves as [formula omitted]. Although the asymptotic behaviour [formula omitted] is not reached in the time region studied by the Monte Carlo method, this distribution explains the long-time behavior of q(t).