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The thermodynamic Bethe Ansatz approach to exactly solvable models in statistical mechanics and quantum field theory

R.M. Ellem

Published Jan 1, 1998• 0 citations
Publisher

Abstract

RSOS models and their associated RZMS scattering QFT models, this is certainly not the case, and here the corresponding TBA equations have been derived only in a few special cases.This shortcoming provides the primary motivation for the work contained in this thesis.After presenting a brief review of the various techniques for deriving the TBA equations associated with the ground state energy for the 0 lj3 perturbations of the minimal CFT models, attempts are made at extending these techniques to the derivation of the TBA equations associated with the ground state energy of the 0 i;2 and perturbations of the minimal CFT models.More recently, the functional relation approach for constructing the ground state TBA equations was extended to the derivation of TBA-like integral equations which correspond to excited state energy levels.In principle, this approach can be used to determine the complete energy spectrum of the perturbed CFT, but in practice this is a very difficult undertaking and only the lowest few excited states are rela tively easily to obtain.In the final chapter of this thesis, this approach is used to determine the TBA-like equations corresponding to the lowest three energy levels of a particular simple perturbed CFT, notably the non-unitary minimal CFT perturbed by its operator <^2,i-L ist o f P u b lic a tio n sThe bulk of the original research content of this thesis is contained in Chapters 4, 5 and 6, with some numerical results tabulated in Appendices B and C. Various parts of this research are, or are soon to be, published as follows.The ground state TBA results of Chapter 5, appear in the paper:• R. M. Ellem, and V. V. Bazhanov: Thermodynamic Bethe Ansatz for the subleading magnetic perturbation of the tricritical Ising Model, Nucl.Phys.B512 (1998), 563-580.The ground state and excited state TBA results of Sections 4.1, 5.1, 5.4 and Chapter 6, and the transfer matrix fusion relations in Section 4.2 and Chapter 6, appear in the paper:• R. M. Ellem, and V. V. Bazhanov: Excited State TBA for the < /> 2,i Perturbed A43;5 Model.To be submitted.The general 5-matrix amplitudes and bootstrap properties of Section 4.3, will ap pear in the paper:• R. M. Ellem: Scattering Structure of the (f)\i2 and (f)2,i Perturbed Minimal Conformal Field Theory Models. Currently in preparation.An extension of the integral equation techniques introduced in Chapter 6, to the fusion equation for the regime 1+ dilute A 2 model described in Section 4.2.1, will appear in the paper:• R. M. Ellem: Excited State TBA for the 02jl Perturbed M .%,4Model.Currently in preparation.

DOI
10.25911/5d63bfb55337c

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We consider the critical nonunitary minimal model M (3, 5) with integrable boundaries and analyze the patterns of zeros of the eigenvalues of the transfer matrix and then determine the spectrum of the critical theory using the thermodynamic Bethe ansatz ( TBA ) equations. Solving the TBA functional equation satisfied by the transfer matrices of the associated A 4 restricted solid-on-solid Forrester–Baxter lattice model in regime III in the continuum scaling limit, we derive the integral TBA equations for all excitations in the ( r , s ) = (1, 1) sector and then determine their corresponding energies. We classify the excitations in terms of ( m , n ) systems .
Abstract The Thermodynamic Bethe Ansatz (TBA) allows us to study finite size and finite temperature effects of an integrable model. This chapter investigates the integral equations that determine the free energy and gives their physical interpretation. It discusses Casimir energy, Bethe relativistic wave function, the derivation of thermodynamics, the meaning of pseudo-energy (dressed energy and momentum), infrared and ultraviolet limits, the coefficient of bulk energy, the general form of the TBA equations, the thermodynamics of the free field theories, L-channel quantization and the LeClair–Mussardo formula. It also covers the application of the Yang–Lee S-matrix, the magnetic field Ising model, and the tricritical Ising model.
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