Scale Invariance and Self-averaging in disordered systems

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

References in corpus (5)

• Critical exponents of the three dimensional diluted Ising model
• Large-q asymptotics of the random bond Potts model
• Scale Invariance in disordered systems: the example of the Random Field Ising Model
• Monte Carlo Study of the Critical Behavior of Random Bond Potts Models
• Multiscaling of energy correlations in the random-bond Potts model

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• Self-Averaging in the Three Dimensional Site Diluted Heisenberg Model at the critical point
• A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model
• Fluids with quenched disorder: Scaling of the free energy barrier near critical points
• Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model
• Nematics with quenched disorder : violation of self-averaging
• Inhomogeneities on all scales at a phase transition altered by disorder