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arXiv:1011.4823 · The European Physical Journal B

Scaling and self-averaging in the three-dimensional random-field Ising model

Nikolaos G. Fytas, A. Malakis

Published Nov 29, 2010• 11 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2010-10404-6

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We show by numerical simulations that the correlation function of the random-field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not self-averaging. This is due to the formation of a bound state in the underlying field theory. We argue that this nonperturbative phenomenon is not particular to the RFIM in 3D. It is generic for disordered systems in two dimensions and may also happen in other three-dimensional disordered systems.
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.