Journal of Statistical Physics

, Volume 33, Issue 2, pp 437–476 | Cite as

Analyticity for one-dimensional systems with long-range superstable interactions

  • M. Campanino
  • D. Capocaccia
  • E. Olivieri


We consider unbounded spin systems and classical continuous particle systems in one dimension. We assume that the interaction is described by a superstable two-body potential with a decay at large distances at least asr−2(lnr)−(2+ε), ε > 0. We prove the analyticity of the free energy and of the correlations as functions of the interaction parameters. This is done by using a “renormalization group technique” to transform the original model into another, physically equivalent, model which is in the high-temperature (small-coupling) region.

Key words

One-dimensional Gibbs systems transfer matrix Markov chains renormalization group decimation procedure cluster expansion 


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Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • M. Campanino
    • 1
  • D. Capocaccia
    • 1
  • E. Olivieri
    • 1
  1. 1.Istituto Matematico “G. Castelnuovo,”Universita degli Studi di RomaRomaItaly

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