FM 2004-3; versione 0.1 31/03/2004

Authors: Alessandro Giuliani, Vieri Mastropietro

Title: Anomalous universality in the Anisotropic Ashkin--Teller model

Abstract: The Ashkin--Teller (AT) model is a generalization of Ising 2--d to a four states spin model; it can be written in the form of two Ising layers (in general with different couplings) interacting via a four--spin interaction. It was conjectured long ago (by Kadanoff and Wegner, Wu and Lin, Baxter and others) that AT has in general two critical points, and that universality holds, in the sense that the critical exponents are the same as in the Ising model, except when the couplings of the two Ising layers are equal (isotropic case). We obtain an explicit expression for the specific heat from which we prove this conjecture in the weakly interacting case and we locate precisely the critical points. We find the somewhat unexpected feature that, despite universality holds for the specific heat, nevertheless nonuniversal critical indexes appear: for instance the distance between the critical points rescales with an anomalous exponent as we let the couplings of the two Ising layers coincide (isotropic limit); and so does the constant in front of the logarithm in the specific heat. Our result also explains how the crossover from universal to nonuniversal behaviour is realized.

Key words: Anisotropic Ashkin-Teller model, nonuniversal critical exponents, renormalization group

Alessandro Giuliani
Fisica, Universita' di Roma "La Sapienza"
P.zzale Aldo Moro
Roma, Italia

Vieri Mastropietro
Matematica, Universita' di Roma 2
Via della Ricerca Scientifica
Roma, Italia