The classical two-dimensional Ising model in the static fluctuation approximation

The classical two-dimensional Ising model is studied in the framework of the so-called static fluctuation approximation. This approximation hinges on the replacement of the square of the local-field operator with its mean value. The physical implication is that the true quantum-mechanical spectrum of this operator is replaced with a distribution; the moments of this distribution as well as the expectation value of the operator are then calculated self-consistently. With this single controllable approximation, the full thermodynamics and the pair correlation function of the classical two-dimensional Ising model are determined for the regular infinite lattice. The possible application to ultrathin ferroelectric films is discussed.