Disorder Averaging and Finite-Size Scaling

Karim Bernardet, Ferenc Pázmándi, and G. G. Batrouni
Phys. Rev. Lett. 84, 4477 – Published 8 May 2000
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Abstract

We propose a new picture of the renormalization group (RG) approach in the presence of disorder, which considers the RG trajectories of each random sample (realization) separately instead of the usual renormalization of the averaged free energy. The main consequence of the theory is that the average over randomness has to be taken after finding the critical point of each realization. To demonstrate these concepts, we study the finite-size scaling properties of the two-dimensional random-bond Ising model. We find that most of the previously observed finite-size corrections are due to the sample-to-sample fluctuation of the critical temperature and scaling predictions are fulfilled only by the new average.

  • Received 22 September 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.4477

©2000 American Physical Society

Authors & Affiliations

Karim Bernardet1, Ferenc Pázmándi2,3, and G. G. Batrouni1

  • 1Institut Non-Linéaire de Nice, Université de Nice-Sophia Antipolis, 1361 route des Lucioles, 06560 Valbonne, France
  • 2Theoretical Physics Department, KLTE, P.O. Box 5, H-4010 Debrecen, Hungary
  • 3Research Group of the Hungarian Academy of Sciences, Institute of Physics, H-1521 TU Budapest, Hungary

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Issue

Vol. 84, Iss. 19 — 8 May 2000

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