Communications in Mathematical Physics

, Volume 108, Issue 2, pp 241–255 | Cite as

One dimensional spin glasses with potential decay 1/r1+g. Absence of phase transitions and cluster properties

  • M. Campanino
  • E. Olivieri
  • A. C. D. van Enter


One-dimensional Ising spin systems interacting via a two-body random potential are considered; a decay with the distance like 1/r1+ε is assumed.

We consider only boundary conditions independent of the random realization of the interactions and prove uniqueness and cluster properties of Gibbs states with probability one.


Boundary Condition Neural Network Phase Transition Statistical Physic Complex System 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • M. Campanino
    • 1
  • E. Olivieri
    • 2
  • A. C. D. van Enter
    • 3
  1. 1.Dipartimento di MatematicaII Università di Roma “Tor Vergata”, via Orazio Raimondo(La Romanina), RomaItaly
  2. 2.Dipartimento di Matematica, Università di Roma “La Sapienza”, p. le A. Moro 5C.N.R.-G.N.F.M.RomaItaly
  3. 3.SFB 123, University of HeidelbergHeidelberg 1Germany

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