A numerical method to compute exactly the partition function with application toZ(n) theories in two dimensions

Abstract

I present a new method to exactly compute the partition function of a class of discrete models in arbitrary dimensions. The time for the computation for ann-state model on anL d lattice scales like\(n^{L^{d - 1} } nL^d \). I show examples of the use of this method by computing the partition function of the 2D Ising and 3-state Potts models for maximum lattice sizes 10×10 and 8×8, respectively. The critical exponentsv andα and the critical temperature one obtains from these are very near the exactly known values. The distribution of zeros of the partition function of the Potts model leads to the conjecture that the ratio of the amplitudes of the specific heat below and above the critical temperature is unity.