Anomalous universality in the anisotropic Ashkin-Teller model
Département de Physique, Université de Princeton
Mon, May. 21st 2007, 14:15
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
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.