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 ${\mathrm{\beta }}_{\mathit{c}}$=0.2656. . . for the two coupled layers of Ising spins. The critical temperature of the three-dimensional Ising model is related to the free energy of the two-layer Ising system.

• Received 17 November 1993

DOI:https://doi.org/10.1103/PhysRevB.49.15023