Time-Dependent Statistics of the Ising Model in a Magnetic Field

Publisher Website
Google Scholar
Abstract
It is of interest to solve the master equation of a one-dimensional Ising model in a magnetic field (Glauber's equation) not only as a mathematical problem, but also for some practical applications. While an exact treatment of Glauber's equation seems impossible, we consider its approximate solutions. We review the applications of the perturbation-expansion method and applications of the mean-field theory to this problem. We also introduce a local-equilibrium method that improves the mean-field theory by taking the short-range correlation into account. The new method yields an analytically soluble differential equation, which, contrary to the preceding two methods, has an exact steady-state solution.