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Journal of Statistical Physics

, Volume 32, Issue 1, pp 141–152 | Cite as

The thermodynamic limit for long-range random systems

  • A. C. D. van Enter
  • J. L. van Hemmen
Articles

Abstract

Long-range spin systems with random interactions are considered. A simple argument is presented showing that the thermodynamic limit of the free energy exists and depends neither on the specific random configuration nor on the sample shape, provided there is no external field. The argument is valid for both classical and quantum spin systems, and can be applied to (a) spins randomly distributed on a lattice and interacting via dipolar interactions; and (b) spin systems with potentials of the formJ(x1,x2)/|x1 -x2| αd , where theJ(x1,x2) are independent random variables with mean zero,d is the dimension, and α > 1/2. The key to the proof is a (multidimensional) subadditive ergodic theorem. As a corollary we show that, for random ferromagnets, the correlation length is a nonrandom quantity.

Key words

Subadditive ergodic theorem random interactions longrange interactions dipolar coupling free energy correlation length 

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Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • A. C. D. van Enter
    • 1
  • J. L. van Hemmen
    • 1
  1. 1.Universität HeidelbergHeidelberg 1Germany

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