The Fokker-Planck equation for the Ising system

Abstract

Starting from the master equation of Glauber (1963), for the Ising system of N spins, and working in the Bragg-Williams approximation, a Fokker-Planck equation is derived for the probability that the system has an overall magnetization. The expansion of the master equation is discussed in powers of N^-1/2 and it is shown that a certain choice of transition probability has to be made to get the correct width of the probability distribution. This is in contrast to the recent work of Goldstein and Scully (1973), which though starting from a Liouville equation effectively works only to the molecular field approximation which is not as satisfactory as the Bragg-Williams approximation. The dynamic magnetic susceptibility is also calculated.