The dilute AL models and the Φ1,2 perturbation of unitary minimal CFTs

Abstract

Motivated by recent studies by Dorey, Pocklington and Tateo for unitary minimal models perturbedby ϕ1,2, we examine the thermodynamics of one-dimensional quantum systems,whose counterparts in the two-dimensional classical model are the diluteAL models in regime 2. The functional relations for arbitrary values ofL are established. Guided by numerical evidence, we obtain a set of coupled integralequations from the established relations, which yields the evaluation of the free energy atarbitrary temperature. In the scaling limit, the integral equations coincide with thethermodynamic Bethe ansatz equations (TBA) proposed by Dorey, Pocklington and Tateo,thereby supporting their results. The new fermionic representations of the Virasorocharacters are remarked upon briefly.