Critical exponents of the four-state Potts model

Abstract

The two-dimensional four-state Potts model at finite temperature can be transformed, via the transfer matrix, into a one-dimensional quantum mechanical model at zero temperature. The duality invariant renormalisation group introduced by Fernandez-Pacheco (1979) is then employed to study the ground-state critical properties of this model. The fixed point is located at exactly the self-dual critical point K*=1. The thermal exponent is calculated to be y_T=1.3219. It is in excellent agreement with the recent series value of Ditzian and Kadanoff (1979) (y_T=1.33). Although it is not inconsistent with den Nijs's (1979) conjectured exact value of ³/₂, the difference is nevertheless substantial.