Finite-Size Scaling and Correlation Lengths for Disordered Systems

J. T. Chayes, L. Chayes, Daniel S. Fisher, and T. Spencer
Phys. Rev. Lett. 57, 2999 – Published 15 December 1986
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Abstract

For a large class of d-dimensional disordered systems, we prove that if an appropriately defined finite-size scaling correlation length diverges at a nontrivial value of the disorder with an exponent ν, then ν must satisfy the bound ν2d. Given the assumption that such a correlation length can be defined, the result applies to, e.g., percolation, disordered magnets, and Anderson localization, both with and without interactions. For localization, this puts stringent constraints on scaling theories and interpretation of experiments.

  • Received 10 September 1986

DOI:https://doi.org/10.1103/PhysRevLett.57.2999

©1986 American Physical Society

Authors & Affiliations

J. T. Chayes and L. Chayes

  • Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853

Daniel S. Fisher

  • AT&T Bell Laboratories, Murray Hill, New Jersey 07974

T. Spencer

  • The Institute for Advanced Study, Princeton, New Jersey 08540

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Vol. 57, Iss. 24 — 15 December 1986

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