Cuesta, José A.Sánchez, Angel2012-07-202012-07-202004-05Journal of Statistical Physics, vol. 115, n. 3-4, mayo 2004. Pp. 869-8930022-4715 (print version)1572-9613 (electronic version)https://hdl.handle.net/10016/14953We 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 theoremapplication/pdfeng© SpringerPhase transitionsOne-dimensional systemsShort-range interactionsTransfer operatorsRigorous resultsresearch articleMatemáticas10.1023/B:JOSS.0000022373.63640.4eopen access869n. 3-4893Journal of Statistical Physicsvol. 115