Exact Partition Functions for the $q$-State Potts Model with a Generalized Magnetic Field on Lattice Strip Graphs

TL;DR

This paper derives exact partition functions for the q-state Potts model on lattice strip graphs with a generalized magnetic field, revealing new symmetry and frustration phenomena in these models.

Contribution

It provides exact solutions for the Potts model with a generalized magnetic field on lattice strips, highlighting novel symmetry and frustration effects.

Findings

Exact partition functions for the Potts model with magnetic field on lattice strips.

Identification of a tensor-product S_s ⊗ S_{q-s} symmetry.

Models exhibit frustration and competing interactions.

Abstract

We calculate the partition function of the $q$-state Potts model on arbitrary-length cyclic ladder graphs of the square and triangular lattices, with a generalized external magnetic field that favors or disfavors a subset of spin values $\{1,...,s\}$ with $s \le q$. For the case of antiferromagnet spin-spin coupling, these provide exactly solved models that exhibit an onset of frustration and competing interactions in the context of a novel type of tensor-product $S_s \otimes S_{q-s}$ global symmetry, where $S_s$ is the permutation group on $s$ objects.