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

TL;DR

This paper supports Smirnov's conjecture on the exact S-matrix for a massive quantum field theory perturbing the tri-critical Ising model, using Thermodynamic Bethe Ansatz and lattice model relations to confirm its properties.

Contribution

It applies the Thermodynamic Bethe Ansatz to the kink scattering theory of the subleading magnetic perturbation of the tri-critical Ising model, providing analytical and numerical validation.

Findings

Recovered the central charge c=0.7 in the ultraviolet limit.

Numerically matched ground state energies with other approaches.

Confirmed the S-matrix conjecture for the perturbation.

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 $\phi_{2,1}$. 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.