D-Dimensional Kinetic S4 Model**The project supported by the National Basic Research Project "Nonlinear Science" and National Natural Science Foundation of China under Grant No. 19775008, and Natural Science Foundation of Jiangxi Province of China under Grant No. 9912001

Abstract

A single-spin transitional critical dynamics based on the Glauber theory is used to investigate the d-dimensional kinetic S4 model. We derive the fundamental dynamical equations by a cumulant expansion, and then, a one-dirnensional model is treated. We obtain approximately the local magnetization and equal-time spin-pair correlation function, in which the terms of k3 and the higher orders are ignored (corresponding to high-temperature cutoff). These are finally extended to d-dimensional case. In addition, we obtain the critical point kc of d-dimensional S4 model, and give a relation satisfied by the dynamic critical exponent z and the correlation length critical exponent ν.