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Journal of Statistical Physics

, Volume 115, Issue 3–4, pp 869–893 | Cite as

General Non-Existence Theorem for Phase Transitions in One-Dimensional Systems with Short Range Interactions, and Physical Examples of Such Transitions

  • José A. Cuesta
  • Angel Sánchez
Article

Abstract

We examine critically the issue of phase transitions in one-dimensional systems with short range interactions. We begin by reviewing in detail the most famous non-existence result, namely van Hove's theorem, emphasizing its hypothesis and subsequently its limited range of applicability. To further underscore this point, we present several examples of one-dimensional short ranged models that exhibit true, thermodynamic phase transitions, with increasing level of complexity and closeness to reality. Thus having made clear the necessity for a result broader than van Hove's theorem, we set out to prove such a general non-existence theorem, widening largely the class of models known to be free of phase transitions. The theorem is presented from a rigorous mathematical point of view although examples of the framework corresponding to usual physical systems are given along the way. We close the paper with a discussion in more physical terms of the implications of this non-existence theorem.

phase transitions one-dimensional systems short-range interactions transfer operators rigorous results 

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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • José A. Cuesta
    • 1
    • 2
  • Angel Sánchez
    • 1
    • 2
  1. 1.Grupo Interdisciplinar de Sistemas Complejos (GISC)Spain
  2. 2.Departamento de MatemáticasUniversidad Carlos III de MadridLeganés, MadridSpain

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