RT Journal Article
T1 General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
A1 Cuesta, José A.
A1 Sánchez, Angel
AB We examine critically the issue of phase transitions in one-dimensional systemswith short range interactions. We begin by reviewing in detail the most famousnon-existence result, namely van Hove’s theorem, emphasizing its hypothesisand subsequently its limited range of applicability. To further underscore thispoint, we present several examples of one-dimensional short ranged models thatexhibit true, thermodynamic phase transitions, with increasing level of complexityand closeness to reality. Thus having made clear the necessity for a resultbroader than van Hove’s theorem, we set out to prove such a general non-existencetheorem, widening largely the class of models known to be free of phasetransitions. The theorem is presented from a rigorous mathematical point ofview although examples of the framework corresponding to usual physicalsystems are given along the way. We close the paper with a discussion in morephysical terms of the implications of this non-existence theorem
PB Springer
SN 0022-4715 (print version)
SN 1572-9613 (electronic version)
YR 2004
FD 2004-05
LK https://hdl.handle.net/10016/14953
UL https://hdl.handle.net/10016/14953
LA eng
NO This work has been supported by the Ministerio de Ciencia y Tecnología of Spain through Grants BFM2000-0004 (JAC) and BFM2000-0006 (AS).
DS e-Archivo
RD 20 jun. 2024