Scale invariance and self-averaging in disordered systems

¹ Dipartimento di Fisica, INFM, SMC and INFN, Università di Roma “La Sapienza” P.le A. Moro 2, 00185 Roma, Italy
² Laboratoire de Physique Théorique et Hautes Energies (Unité Mixte de Recherche CNRS UMR 7589, associée à l'Université Pierre et Marie Curie, Paris VI et à l'Université Denis Diderot, Paris VII.) - Boîte 126 Tour 16, 1er étage, 4 place Jussieu, F-75252 Paris Cedex 05, France
³ Laboratoire de Physique Théorique de l'Ecole Normale Supérieure (Unité Mixte de Recherche du CNRS et de l'Ecole Normale Supérieure, associée à l'Université Pierre et Marie Curie, Paris VI.) 24 rue Lhomond, 75231 Paris Cedex 05, France

Received: 5 January 2004
Accepted: 8 March 2004

Abstract

In a previous paper (Parisi G. and Sourlas N., Phys. Rev. Lett. 89 (2002) 257204) we found that in the random field Ising model at zero temperature in three dimensions the correlation length is not self-averaging near the critical point and that the violation of self-averaging is maximal. This is due to the formation of bound states in the underlying field theory. We present a similar study for the case of disordered Potts and Ising ferromagnets in two dimensions near the critical temperature. In the random Potts model the correlation length is not self-averaging near the critical temperature but the violation of self-averaging is weaker than in the random field case. In the random Ising model we find still weaker violations of self-averaging and we cannot rule out the possibility of the restoration of self-averaging in the infinite volume limit.