Large and small Density Approximations to the thermodynamic Bethe Ansatz

Details Large and small Density Approximations to the thermodynamic Bethe Ansatz Large and small Density Approximations to the thermodynamic Bethe Ansatz

2000-02-22

arxiv.org/abs/hep-th/0002185v1

Nucl.Phys. B579 (2000) 617-631

Physics

High Energy Physics

High Energy Physics - Theory

19 pages Latex, 2 figures

Scientific paper

10.1016/S0550-3213(00)00250-9

We provide analytical solutions to the thermodynamic Bethe ansatz equations in the large and small density approximations. We extend results previously obtained for leading order behaviour of the scaling function of affine Toda field theories related to simply laced Lie algebras to the non-simply laced case. The comparison with semi-classical methods shows perfect agreement for the simply laced case. We derive the Y-systems for affine Toda field theories with real coupling constant and employ them to improve the large density approximations. We test the quality of our analysis explicitly for the Sinh-Gordon model and the $(G_2^{(1)},D_4^{(3)})$-affine Toda field theory.

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