Potts model on recursive lattices: some new exact results

TL;DR

This paper derives exact partition functions for the Potts model on various recursive lattices, including square, diced, Kagome, and others, revealing new analytical results and insights into their phase behavior.

Contribution

It provides new exact solutions for the Potts model on multiple recursive lattices with different widths and structures, expanding the understanding of these models.

Findings

Exact partition functions for square, diced, and Kagome lattices.

Analysis of Fisher zeros and large q-limit behavior.

New insights into phase transitions on recursive lattices.

Abstract

We compute the partition function of the Potts model with arbitrary values of $q$ and temperature on some strip lattices. We consider strips of width $L_y=2$, for three different lattices: square, diced and `shortest-path' (to be defined in the text). We also get the exact solution for strips of the Kagome lattice for widths $L_y=2,3,4,5$. As further examples we consider two lattices with different type of regular symmetry: a strip with alternating layers of width $L_y=3$ and $L_y=m+2$, and a strip with variable width. Finally we make some remarks on the Fisher zeros for the Kagome lattice and their large q-limit.