2003/06/30 by Jose A. Cuesta, José A. Cuesta, Ángel Sánchez +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #nlin.AO #physics.class-ph
paper · pdf · doi:10.1023/b:joss.0000022373.63640.4e
Short comment on possible generalization to wider classes of systems added; accepted for publication in Journal of Statistical Physics
arxiv created 2003/11/11 · openalex publication_date 2004/04/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.