Nonlinear Integral Equations and high temperature expansion for the $U_{q}(\hat{sl}(r+1|s+1))$ Perk-Schultz Model

Details Nonlinear Integral Equations and high temperature expansion for the $U_{q}(\hat{sl}(r+1|s+1))$ Perk-Schultz Model Nonlinear Integral Equations and high temperature expansion for the $U_{q}(\hat{sl}(r+1|s+1))$ Perk-Schultz Model

2005-10-18

arxiv.org/abs/cond-mat/0510458v1

Nucl.Phys.B737:261-290,2006

Physics

Condensed Matter

Statistical Mechanics

35 pages, 3 eps figures

Scientific paper

10.1016/j.nuclphysb.2005.12.017

We propose a system of nonlinear integral equations (NLIE) which gives the free energy of the $U_{q}(widehat{sl}(r+1|s+1))$ Perk-Schultz model. In contrast with traditional thermodynamic Bethe ansatz equations, our NLIE contain only r+s+1 unknown functions. In deriving the NLIE, the quantum (supersymmetric) Jacobi-Trudi and Giambelli formula and a duality for an auxiliary function play important roles. By using our NLIE, we also calculate the high temperature expansion of the free energy. General formulae of the coefficients with respect to arbitrarily rank r+s+1, chemical potentials $\{\mu_{a}\}$ and q have been written down in terms of characters up to the order of 5. In particular for specific values of the parameters, we have calculated the high temperature expansion of the specific heat up to the order of 40.

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