1. Scale Invariance and Self-averaging in disordered systems
- Author
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Nicolas Sourlas, Giorgio Parisi, Marco Picco, Dipartimento di Fisica, La Sapienza, Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome], Laboratoire de Physique Théorique et Hautes Energies (LPTHE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome] (UNIROMA), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Physics ,Self-averaging ,Random field ,Statistical Mechanics (cond-mat.stat-mech) ,FOS: Physical sciences ,General Physics and Astronomy ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Scale invariance ,Condensed Matter - Disordered Systems and Neural Networks ,01 natural sciences ,Condensed Matter::Disordered Systems and Neural Networks ,010305 fluids & plasmas ,05.10, 05.20, 75.10, 75.40 ,Ferromagnetism ,Critical point (thermodynamics) ,0103 physical sciences ,Bound state ,Ising model ,[PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn] ,Statistical physics ,[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] ,010306 general physics ,Condensed Matter - Statistical Mechanics ,Potts model - Abstract
In a previous paper 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., 7 pages, 4 ps figures
- Published
- 2003
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