Communications in Mathematical Physics

, Volume 66, Issue 2, pp 147–166 | Cite as

Phase transitions in ferromagnetic spin systems at low temperatures

  • W. Holsztynski
  • J. Slawny


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.


Neural Network Phase Transition Statistical Physic Equilibrium State Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • W. Holsztynski
    • 1
  • J. Slawny
    • 2
  1. 1.Department of MathematicsThe University of Western OntarioLondonCanada
  2. 2.Department of MathematicsRutgers UniversityNew BrunswickUSA

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