Square lattice variational approximations applied to the Ising model

The variational method developed by Baxter is applied to the zero-field Ising model on the square lattice. The problem is simplified to that of solving a relatively small system of nonlinear equations. The estimates to the spontaneous magnetization and the critical temperature from the sequence of variational approximations are obtained. The results converge rapidly to the exact ones. They exhibit a crossover phenomenon and satisfy a scaling relation.