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Phase transitions in ferromagnetic spin systems at low temperatures

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Abstract

We consider the problem of the existence of first order phase transitions in ferromagnetic spin systems at low temperatures. A criterion is given for the existence of phase transitions in terms of an algebraic system canonically associated with any interaction. The criterion involves finding out if the greatest common divisor of few polynomials belongs to the ideal generated by these polynomials.

In connection with results published earlier, this work yields a description of all translation invariant (also of periodic and quasi-periodic) equilibrium states at low temperatures.

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Authors and Affiliations

  1. Department of Mathematics, The University of Western Ontario, NGA 5B9, London, Canada

    W. Holsztynski

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey, USA

    J. Slawny

Authors
  1. W. Holsztynski
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  2. J. Slawny
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Communicated by E. Lieb

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Holsztynski, W., Slawny, J. Phase transitions in ferromagnetic spin systems at low temperatures. Commun.Math. Phys. 66, 147–166 (1979). https://doi.org/10.1007/BF01197332

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  • DOI: https://doi.org/10.1007/BF01197332

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