Variational method and duality in the 2D square Potts model

TL;DR

This paper introduces a variational method for analyzing the 2D q-state Potts model, ensuring duality relations are exactly satisfied and providing accurate numerical estimates across all temperatures.

Contribution

It develops an operatorial variational approach that exactly incorporates duality, improving numerical estimates for the Potts model beyond previous methods.

Findings

Exact duality relations are satisfied in the variational approach

Numerical estimates are accurate across all temperature ranges

Method can be systematically refined for better results

Abstract

The ferromagnetic q-state Potts model on a square lattice is analyzed, for q>4, through an elaborate version of the operatorial variational method. In the variational approach proposed in the paper, the duality relations are exactly satisfied, involving at a more fundamental level, a duality relationship between variational parameters. Besides some exact predictions, the approach is very effective in the numerical estimates over the whole range of temperature and can be systematically improved.