Anti-Symmetrically Fused Model and Non-Linear Integral Equations in the Three-State Uimin-Sutherland Model

TL;DR

This paper derives and solves non-linear integral equations for the three-state Uimin-Sutherland model, revealing low-temperature behavior consistent with conformal field theory and calculating key magnetic properties.

Contribution

It introduces an anti-symmetric fusion procedure to derive a complete set of auxiliary functions for the model.

Findings

Low-temperature behavior matches conformal field theory predictions

Magnetization and susceptibility are successfully computed

Numerical solutions confirm theoretical expectations

Abstract

We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation.