The dilute AL models and the integrable perturbations of unitary minimal CFTs

Recently, a set of thermodynamic Bethe ansatz (TBA) equations has been proposed by Dorey, Pocklington and Tateo for unitary minimal models perturbed by the 1,2 or 2,1 operator. We examine their results in view of the lattice analogues, dilute AL models in regimes 1 and 2. Taking M5,6 + 1,2 and M3,4 + 2,1 as the simplest examples, we will explicitly show that the conjectured TBA equations can be recovered from the lattice model in a scaling limit.