Coherent-Anomaly Method in Critical Phenomena. V. Estimation of the Dynamical Critical ExponentΔof the Two-Dimensional Kinetic Ising Model

Abstract

The coherent-anomaly method (CAM) is applied to the kinetic Ising model. Dynamical cluster-mean-field approximations are formulated to obtain a series of the dynamical mean-field critical coefficients. The coherent-anomaly scaling relations are derived on the basis of the scaling form of the generating function in nonequilibrium systems to estimate the exponent Δ of the critical slowing down. The dynamical critical exponent is estimated as \({\varDelta}{\backsimeq}2.15({\pm}0.02)\) for the kinetic Ising model on the two-dimensional triangular lattice.