Dynamics of the Ising Model near the Critical Point. I

Abstract

A simple dynamical model of interacting Ising spins is discussed. Each spin is assumed to flip spontaneously with a transition probability which depends on the temperature and the configuration of surrounding spins, but its functional form is assumed to be the simplest. The frequency-wave number dependent susceptibility χ( q , ω) is given exactly in the one-dimensional case. In two-and three-dimensional cases the model is treated in the molecular field and the generalized approximations.