Finite-size scaling and correlation lengths for disordered systems

Journal Article · Mon Dec 15 00:00:00 EST 1986 · Phys. Rev. Lett.; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.57.2999· OSTI ID:6743670

Chayes, J T; Chayes, L; Fisher, D S; Spencer, T

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 ..nu.., then ..nu.. must satisfy the bound ..nu..greater than or equal to2/d. 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.

• Research Organization: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853
• OSTI ID: 6743670
• Journal Information: Phys. Rev. Lett.; (United States), Vol. 57:24
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
PHASE TRANSFORMATIONS
SCALING LAWS
CORRELATIONS
FERROMAGNETIC MATERIALS
HAMILTONIANS
ISING MODEL
CRYSTAL MODELS
MAGNETIC MATERIALS
MATERIALS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
657000* - Theoretical & Mathematical Physics