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A study of metastability in the Ising model

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Abstract

We consider a two-dimensional Ising ferromagnet with (+) boundary conditions and negative external field, where a Markovian time evolution is assumed.

We construct, suitably restricting the allowed configurations att=0, a non equilibrium state with positive magnetization such that:

  1. 1)

    only one phase is present,

  2. 2)

    the relaxation time for unit volume is finite and can be made very large.

These results are obtained following a general method for describing metastable states proposed by Lebowitz and Penrose and exploiting the analysis of the Ising-spin-configurations in terms of contours given by Minlos and Sinai.

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Authors and Affiliations

  1. GNSM-CNR, Istituto di Fisica, dell'Università di Roma, Roma

    D. Capocaccia

  2. Istituto Universitario Navale, Napoli, Italy

    D. Capocaccia

  3. Istituto di Fisica dell'Università di Roma, Roma

    M. Cassandro

  4. Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Roma, Italy

    M. Cassandro

  5. Istituto di Matematica dell'Università di Roma, Roma

    E. Olivieri

  6. C.N.R., Gruppo Nazionale Fisica Matematica, Roma, Italy

    E. Olivieri

Authors
  1. D. Capocaccia
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  2. M. Cassandro
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  3. E. Olivieri
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Communicated by J. L. Lebowitz

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Capocaccia, D., Cassandro, M. & Olivieri, E. A study of metastability in the Ising model. Commun.Math. Phys. 39, 185–205 (1974). https://doi.org/10.1007/BF01614240

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  • DOI: https://doi.org/10.1007/BF01614240

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