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Scale Invariance and Self-averaging in disordered systems

Giorgio Parisi·Marco Picco·Nicolas Sourlas
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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.

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BibTeXRIS

Giorgio Parisi, Marco Picco, Nicolas Sourlas. 2003-12-31. Scale Invariance and Self-averaging in disordered systems. https://doi.org/10.1209/epl%2Fi2004-10014-0

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