New correlated-effective-field theory in the Ising model

A new method incorporating the effects of many-body static spin correlations into an effective-field theory is discussed. The method is based on the introduction of a differential operator and the concept of the correlated effective field into two exact Callen identities of the Ising model. The resulting statistical theory is shown to have an accuracy equivalent to that of the Bethe-Peierls method. It is shown that the correlated-effective-field parameter at the transition temperature has a universal function of $\frac{1}{\mathrm{}(z-1\mathrm{})\mathrm{}}$, where $z$ is the number of nearest neighbors.