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Disorder Averaging and Finite Size Scaling

By Karim Bernardet, Ferenc Pazmandi and G. G. Batrouni

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 is more adequate in terms of the new scaling variables.Comment: 4 pages, 6 figures include

Topics: Condensed Matter - Statistical Mechanics
Publisher: 'American Physical Society (APS)'
Year: 1999
DOI identifier: 10.1103/PhysRevLett.84.4477
OAI identifier: oai:arXiv.org:cond-mat/9909299

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