Disorder Averaging and Finite Size Scaling

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.

4 pages, 6 figures included

References in corpus (3)

• Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems
• The Random Transverse Ising Spin Chain and Random Walks
• Revisiting the Theory of Finite Size Scaling in Disordered Systems: νCan Be Less Than 2/d

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