Some New Exact Results for the q-State Potts Model on Ladder Graphs

TL;DR

This paper provides exact calculations of the partition function for the q-state Potts model on ladder graphs, introducing a new transfer matrix representation that facilitates determinant calculations for arbitrary lattice sizes.

Contribution

It introduces a novel transfer matrix representation for the q-state Potts model on ladder graphs, enabling exact partition function calculations for general q, temperature, and magnetic field.

Findings

Exact partition functions for ladder graphs with periodic boundary conditions.

A new transfer matrix representation for the Potts model.

Determinant calculations for arbitrary lattice sizes.

Abstract

We present exact calculations of the partition function for the q-state Potts model for general q, temperature and magnetic field on strips of the square lattices of width $L_{y}=2$ and arbitrary length $L_x = m $ with periodic longitudinal boundary conditions. A new representation of the transfer matrix for the q-state Potts model is introduced which can be used to calculate the determinant of the transfer matrix for an arbirary $m \times m$ lattice with periodic boundary conditions.