A simple formula for the critical temperature of D-dimensional Ising models

We propose a simple equation for the critical temperature (CT) of D-dimensional Ising models (on squared or not squared lattices). When 2 < D < infinity, these models have no exact solution and even the simpler problem of locating the CT analytically remains a formidable task. The mean-field as well as the belief-propagation methods provide approximations that work only for large D, remaining quite unsatisfactory for D <= 4. Our simple equation represents a sort of 'finite-dimensional' generalization of such approaches. It provides a reasonable approximation for D = 2 and works pretty well for D >= 3 where, in general, outperforms other purely analytical methods. The equation is derived by using duality relations and heuristic arguments.