Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model
Statistical Mechanics
2008-11-26 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We derive traditional thermodynamic Bethe ansatz (TBA) equations for the sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer matrix. These TBA equations are identical to the ones from the string hypothesis. Next we derive a new family of nonlinear integral equations (NLIE). In particular, a subset of these NLIE forms a system of NLIE which contains only a finite number of unknown functions. For r=1, this subset of NLIE reduces to Takahashi's NLIE for the XXX spin chain. A relation between the traditional TBA equations and our new NLIE is clarified. Based on our new NLIE, we also calculate the high temperature expansion of the free energy.
Keywords
Cite
@article{arxiv.cond-mat/0212280,
title = {Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model},
author = {Zengo Tsuboi},
journal= {arXiv preprint arXiv:cond-mat/0212280},
year = {2008}
}
Comments
24 pages, 4 figures, to appear in J. Phys. A: Math. Gen