Nonlinear Integral Equations for Thermodynamics of the U_{q}(\hat{sl(r+1)}) Perk-Schultz Model

TL;DR

This paper introduces a new system of nonlinear integral equations to describe the thermodynamics of the U_{q}(\hat{sl(r+1)}) Perk-Schultz model, extending previous results and enabling high-temperature expansion calculations.

Contribution

The authors develop a simplified set of NLIE with only r unknown functions for the model, generalizing earlier work and including high-temperature free energy coefficients.

Findings

Derived NLIE for the model's thermodynamics.

Reduced to Takahashi's NLIE for r=1.

Calculated high-temperature free energy coefficients up to order 99.

Abstract

We propose a system of nonlinear integral equations (NLIE) which describes the thermodynamics of the U_{q}(\hat{sl(r+1)}) Perk-Schultz model. These NLIE correspond to a trigonometric analogue of our previous result (cond-mat/0212280), and contain only r unknown functions. In particular, they reduce to Takahashi's NLIE for the XXZ spin chain (cond-mat/0010486) if r=1. We also calculate the high temperature expansion of the free energy. In particular for r=1 case, we have succeeded to derive the coefficients of order O((\frac{J}{T})^{99}).