The replica momenta of a spin-glass and the phase diagram of n-colour Ashkin-Teller models

Abstract

Some properties of the phase diagrams of the finite replica momenta for an Ising spin-glass are studied, using exact results on n-colour Ashkin-Teller models. In the two-dimensional case the second replica momentum exhibits continuously varying critical exponents and the tricritical point is found to lie on the Nishimori's line. We obtain the width of the probability distribution of the partition function on particular lines of the phase diagram. We point out an exact relation between the n and ( n + 1) th replica momenta, valid for arbitrary dimensions, which implies a symmetry property of the phase diagram. This allows to verify the nice agreement of some predictions of the « generalized random energy model » with these exact results