Excited TBA Equations II: Massless Flow from Tricritical to Critical Ising Model

TL;DR

This paper derives and solves massless thermodynamic Bethe ansatz equations to describe the renormalization group flow from the tricritical to the critical Ising model in a cylindrical geometry, including boundary conditions.

Contribution

It provides the first derivation of massless TBA equations for all excitations in this flow, extending previous massive case results and classifying excitations via (m,n) systems.

Findings

Successfully derived massless TBA equations for the flow

Numerically solved equations to track flow from UV to IR fixed points

Confirmed flow of characters from tricritical to critical Ising models

Abstract

We consider the massless tricritical Ising model M(4,5) perturbed by the thermal operator 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 massless 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 IV. The resulting TBA equations describe the massless renormalization group flow from the tricritical to critical Ising model. As in the massive case of Part I, the excitations are completely classified in terms of (m,n) systems but the string content changes by one of three mechanisms along the flow. Using generalized q-Vandemonde identities, we show that this leads to a flow from tricritical to critical Ising characters. The excited TBA equations are solved numerically to follow the continuous flows from the UV to the IR conformal fixed points.