Locating analytically critical temperature in some statistical systems

Abstract

We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and $Z(N<5)$ models. It also works for the Ising model on the triangular lattice. For systems which are not selfdual 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.