The dilute A_L models and the Phi_{1,2} perturbation of unitary minimal CFTs

TL;DR

This paper investigates the thermodynamics of dilute A_L models in regime 2, establishing functional relations and integral equations that align with known TBA equations, thus advancing understanding of perturbed minimal CFTs.

Contribution

It derives functional relations and integral equations for dilute A_L models, confirming their connection to TBA equations in the scaling limit and providing new Fermionic representations of Virasoro characters.

Findings

Functional relations for dilute A_L models established.

Integral equations match TBA equations in the scaling limit.

Supports previous TBA results for perturbed minimal models.

Abstract

Motivated by recent studies by Dorey, Pocklington and Tateo for unitary minimal models perturbed by phi_{1,2}, we examine the thermodynamics of one dimensional quantum systems, whose counterparts in the 2D classical model are the dilute A_L models in regime 2. The functional relations for arbitrary values of L are established. Guided by numerical evidences, we obtain a set of coupled integral equations from the established relations, which yields the evaluation of the free energy at arbitrary temperature. In the scaling limit, the integral equations coincide with the thermodynamic Bethe ansatz equations (TBA) proposed in {DPT2}, thereby support their results. The new Fermionic representations of the Virasoro characters are shortly remarked.