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

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Abstract

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

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Author notes

  1. A. C. D. van Enter

    Present address: Department of Physics Technion, Technion City, A.C.D. van Enter, Il-32000, Haifa, Israel

Authors and Affiliations

  1. Dipartimento di Matematica, II Università di Roma “Tor Vergata”, via Orazio Raimondo, I-00173, (La Romanina), Roma, Italy

    M. Campanino

  2. Dipartimento di Matematica, Università di Roma “La Sapienza”, p. le A. Moro 5, C.N.R.-G.N.F.M., I-00185, Roma, Italy

    E. Olivieri

  3. SFB 123, University of Heidelberg, Im Neuenheimer Feld 294, D-6900, Heidelberg 1, Germany

    A. C. D. van Enter

Authors
  1. M. Campanino
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  2. E. Olivieri
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  3. A. C. D. van Enter
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Additional information

Communicated by T. Spencer

Partially supported by GNAFA of CNR

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Campanino, M., Olivieri, E. & van Enter, A.C.D. One dimensional spin glasses with potential decay 1/r 1+g. Absence of phase transitions and cluster properties. Commun.Math. Phys. 108, 241–255 (1987). https://doi.org/10.1007/BF01210614

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  • DOI: https://doi.org/10.1007/BF01210614

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