Publication: General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
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ISSN: 0022-4715 (print version)
ISSN: 1572-9613 (electronic version)
Publication date
2004-05
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Tutors
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Springer
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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
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Keywords
Phase transitions, One-dimensional systems, Short-range interactions, Transfer operators, Rigorous results
Bibliographic citation
Journal of Statistical Physics, vol. 115, n. 3-4, mayo 2004. Pp. 869-893