The Ashkin-Teller model is a two dimensional spin system, in which two Ising layers interact via a four-spin interaction. We consider the case of weak anisotropy (slight a-symmetry between the two Ising layers) and weak coupling. We show that the system admits two critical temperatures whose difference varies continuously with the strength of the coupling, scaling with an anomalous exponent. The specific heat diverges logarithmically at the critical points (as for Ising) but the constant in front of the logarithm is renormalized by an anomalous critical exponent. The result provides a detailed description of the universality/non-universality crossover in the Ashkin-Teller model. The proof is based on an exact mapping to a $1+1$ dimensional fermionic system and a Renormalization Group analysis of the effective fermionic action. The method is suitable for studying scaling limits and thermodynamic behavior at the critical point for a large class of perturbed 2D Ising models. The talk is based on a joint work with V. Mastropietro.

Département de Physique, Université de Princeton