Character decomposition of Potts model partition functions. II. Toroidal geometry

TL;DR

This paper extends a combinatorial method for decomposing the Potts model partition function to toroidal geometries, providing a systematic way to determine eigenvalue amplitudes and degeneracies.

Contribution

It introduces a new approach to decompose the Potts model partition function on toroidal lattices using characters labeled by bridges and symmetric group representations.

Findings

Decomposition method for toroidal boundary conditions

Operational technique for eigenvalue amplitudes

Determination of degeneracies of eigenvalues

Abstract

We extend our combinatorial approach of decomposing the partition function of the Potts model on finite two-dimensional lattices of size L x N to the case of toroidal boundary conditions. The elementary quantities in this decomposition are characters K\_{l,D} labelled by a number of bridges l=0,1,...,L and an irreducible representation D of the symmetric group S\_l. We develop an operational method of determining the amplitudes of the eigenvalues as well as some of their degeneracies.