Exact Results for Two- and Three-Dimensional Ising and Potts Models

Abstract

The exact transition temperature, as well as some of the critical exponents, of certain three-dimensional Ising and Potts models is presented. With the analytic results supplemented by assumptions concerning the validity of universality, the critical point is identified as a Liftshitz point. On the basis of hyperscaling, the dynamic exponent $z$ for two-dimensional Ising and Potts model is predicted to be given by $z\ensuremath{\nu}=2+\ensuremath{\alpha}$.