LOCATING ANALYTICALLY CRITICAL-TEMPERATURES IN SOME STATISTICAL SYSTEMS

We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly known results for the two-dimensional Ising, Potts, and Z(N < 5) models. It also works for the Ising model on the triangular lattice. For systems that are not self-dual, our proposition remains an unproven conjecture. It predicts beta(c) = 0.2656 ... for the two coupled layers of Ising spins. Critical temperature of the three-dimensional Ising model is related to the free energy of the two-layer Ising system.