Excited TBA Equations I: Massive Tricritical Ising Model

TL;DR

This paper derives and analyzes massive thermodynamic Bethe ansatz equations for the perturbed tricritical Ising model with boundary conditions, elucidating the spectrum and flows between conformal and massive regimes.

Contribution

It provides the first derivation of TBA equations for all excitations in the massive tricritical Ising model with boundary conditions, extending integrable methods off-critical.

Findings

Classification of excitations matches conformal point

Determination of UV and IR spectra

Analysis of massive flows and boundary effects

Abstract

We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator phi_{1,3} in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A_4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m,n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r,s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters chi_{r,s}(q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II.