Absence of Self-Averaging and Universal Fluctuations in Random Systems near Critical Points

Amnon Aharony and A. Brooks Harris
Phys. Rev. Lett. 77, 3700 – Published 28 October 1996
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Abstract

The distributions P(X) of singular thermodynamic quantities, on an ensemble of d-dimensional quenched random samples of linear size L near a critical point, are analyzed using the renormalization group. For L much larger than the correlation length ξ, we recover strong self-averaging (SA): P(X) approaches a Gaussian with relative squared width RX(L/ξ)d. For Lξ we show weak SA ( RX decays with a small power of L) or no SA [ P(X) approaches a non-Gaussian, with universal L-independent relative cumulants], when the randomness is irrelevant or relevant, respectively.

  • Received 1 August 1996

DOI:https://doi.org/10.1103/PhysRevLett.77.3700

©1996 American Physical Society

Authors & Affiliations

Amnon Aharony1 and A. Brooks Harris2

  • 1School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
  • 2Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104

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Vol. 77, Iss. 18 — 28 October 1996

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