Thermodynamic Bethe Ansatz for the subleading magnetic perturbation of the tricritical Ising model

TL;DR

This work tests Smirnov's kink $S$-matrix conjecture for the integrable perturbation of the TIM by $\phi_{2,1}$ (with $(\Delta,\bar{\Delta})=(7/16,7/16)$ and $c=0.7$) by developing a Thermodynamic Bethe Ansatz for the kink scattering theory, using its link to the lattice hard hexagon model. The authors derive a novel three-component TBA system, confirm the ultraviolet energy scaling $E(R)\sim -\pi c/(6R)$ with $c=0.7$, and demonstrate quantitative agreement with TCSA and CPT for the ground-state energy of finite-size systems. They also discuss extensions to RSOS models and related perturbations, and outline prospects for excited-state TBA and connections to twisted Kac–Moody algebras. Overall, the paper provides a robust finite-size analysis validating the proposed kink $S$-matrix and broadens the exact, integrable-QFT toolkit for minimal-model perturbations.

Abstract

We give further support to Smirnov's conjecture on the exact kink S-matrix for the massive Quantum Field Theory describing the integrable perturbation of the c=0.7 minimal Conformal Field theory (known to describe the tri-critical Ising model) by the operator $φ_{2,1}$. This operator has conformal dimensions $(7/16,7/16)$ and is identified with the subleading magnetic operator of the tri-critical Ising model. In this paper we apply the Thermodynamic Bethe Ansatz (TBA) approach to the kink scattering theory by explicitly utilising its relationship with the solvable lattice hard hexagon model. Analytically examining the ultraviolet scaling limit we recover the expected central charge c=0.7 of the tri-critical Ising model. We also compare numerical values for the ground state energy of the finite size system obtained from the TBA equations with the results obtained by the Truncated Conformal Space Approach and Conformal Perturbation Theory.

Figures (1)

• Figure 1: The ground state energy $E(R)$ (given in units of mass $m$) computed from the TBA equations (\ref{['eq:tbae']}),(\ref{['eq:eofr']}), from the TCSA method strip, and from the first three terms of the CPT short distance expansion (\ref{['cptexp']}), plotted against the dimensionless variable $mR$.