Coherent-Anomaly Method in Critical Phenomena.

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 Δ ≃ 2.15 (±0.02) for the kinetic Ising model on the two-dimensional triangular lattice.