New Approximate Method for Ising System

Abstract

A new approximate treatment of the Ising spins is presented, in which the fluctuation of the effective field is taken into consideration. It is shown that the simplest approximation gives the satisfactory results. The approximation is applied to the random spin system and the critical concentration is calculated. The results are again satisfactory compared with those of other method. This idea is applied to the dynamical problem based upon the Galuber model, and it is shown that the approximation equivalent to Bethe's one can be obtained in the case of the thermal equilibrium by the improvement of the simplest approximation. Using the improved approximation, the dynamical susceptibility and the pair correlation function in the thermal equilibrium are calculated.