A mean-field equation for a cosine interaction on a lattice

We derive a mean-field equation for the :cos(αΨ):c interacting system on a lattice of arbitrary dimensionality. A new expansion is introduced to improve the convergence of the summation appearing in the equation. We solve the equation numerically and compare it to the classical solutions of the problem. We find that for low dimensionality the mean field solutions differ significantly from the classical solution, while for high dimensionality they approach the simple form of the classical soluton.