Approximate calculations for the two-dimensional Ising model

Abstract

A self-consistent molecular field approximation for the two-dimensional, square-lattice Ising model is used to calculate the energy and magnetization. Agreement with the exact calculations is good except near the critical temperature, which differs from the exact critical temperature by 4%. The specific heat has no anomalous behavior asT approachesT _c from above, and the magnetization follows the incorrect Weiss (T _c-T)^1/2 law asT approachesT _c from below.