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arXiv:hep-th/0206134 · Journal of Physics A Mathematical and General

Thermodynamics of the criticalRSOS(q1,q2;q) model

Anastasia Doikou

Published Dec 17, 2002• 3 citations
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Abstract

The thermodynamic Bethe ansatz method is employed for the study of the integrable critical RSOS ( q 1 , q 2 ; q ) model. The high and low temperature behaviours are investigated, and the central charge of the effective conformal field theory is derived. The obtained central charge is expressed as the sum of the central charges of two generalized coset models.

DOI
10.1088/0305-4470/36/2/303

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The thermodynamic Bethe ansatz method is employed for the study of the integrable critical RSOS ( q 1 , q 2 ; q ) model. The high and low temperature behaviours are investigated, and the central charge of the effective conformal field theory is derived. The obtained central charge is expressed as the sum of the central charges of two generalized coset models.
We present a computational framework not based on the string hypothesis for the thermodynamics of statistical and quantum field theory models solvable by the Bethe ansatz. In the cases of XXZ Heisenberg chain and the sine-Gordon quantum field theory we derive a single nonlinear integral equation which determines the free energy (or ground-state scaling function). Our approach is very effective at high temperature, and correctly reproduces the low-temperature central charge and the analytic structure of the corrections.
We show that the criticality of integrable lattice models based on the Lie algebras An{\mathit{A}}_{\mathit{n}}An​,Dn{\mathit{D}}_{\mathit{n}}Dn​,En{\mathit{E}}_{\mathit{n}}En​ can be understood as the product of certain numbers of bosonic fields and a generalized parafermionic (fractional spin) theory (GPT). We compute the central charge of the GPT using the thermodynamic Bethe-ansatz approach. For the model associated with the A2{\mathit{A}}_{2}A2​ Lie algebra, we propose that the associated GPT can be described by a composition of Ising and tricritical-Ising conformal field theories.
We present a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisemberg chain we derive, for arbitrary values of the anysotropy, a {\bf single} non--linear integral equation from which the free energy can be exactly calculated. The high--temperature expansion follows in a sistematic and relatively simple way. For low temperatures we obtain the correct central charge and predict the analytic structure of the full expansion around T=0T=0T=0. Furthermore, we derive a single non-linear integral equation describing the finite--size ground--state energy of the Sine--Gordon quantum field theory. PACS: 05.30, 03.70. 75.10.5
The study of the scaling limit of two-dimensional models of statistical mechanics within the framework of integrable field theory is illustrated through the example of the RSOS models. Starting from the exact description of regime III in terms of colliding particles, we compute the correlation functions of the thermal, phi1,2\\phi_{1,2}phi1,2​ and (for some cases) spin operators in the two-particle approximation. The accuracy obtained for the moments of these correlators is analysed by computing the central charge and the scaling dimensions and comparing with the exact results. We further consider the (generally non-integrable) perturbation of the critical points with both the operators phi1,3\\phi_{1,3}phi1,3​ and phi1,2\\phi_{1,2}phi1,2​ and locate the branches solved on the lattice within the associated two-dimensional phase diagram. Finally we discuss the fact that the RSOS models, the dilute qqq-state Potts model at and the O(n) vector model are all described by the same perturbed conformal field theory.