d-dimensional kinetic S-4 model

A single-spin transitional critical dynamics based on the Glauber theory is used to investigate the d-dimensional kinetic S-4 model. We derive the fun damental dynamical equations by a cumulant expansion, and then, a one-dimen sional model is treated. We obtain approximately the local magnetization an d equal-time spin-pair correlation function, in which the terms of k(3) and the higher orders are ignored (corresponding to high-temperature cutoff). These are finally extended to d-dimensional case. In addition, we obtain th e critical point k(c) of d-dimensional S-4 model, and give a relation satis fied by the dynamic critical exponent z and the correlation length critical exponent nu.