Thermodynamics of the Farey Fraction Spin Chain

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dc.creatorFiala, Jan
dc.creatorKleban, Peter
dc.date2003-10-09
dc.date2004-02-16
dc.date.accessioned2026-07-07T08:11:41Z
dc.date.available2026-07-07T08:11:41Z
dc.descriptionWe consider the Farey fraction spin chain, a one-dimensional model defined on (the matrices generating) the Farey fractions. We extend previous work on the thermodynamics of this model by introducing an external field $h$. From rigorous and renormalization group arguments, we determine the phase diagram and phase transition behavior of the extended model. Our results are fully consistent with scaling theory (for the case when a "marginal" field is present) despite the unusual nature of the transition for h=0.
dc.description20 pages, 5 figures, revtex4, proof completed in section III, added appendix and 2 references; accepted by Journal of Statistical Physics
dc.identifierhttps://arxiv.org/abs/math-ph/0310016
dc.identifierhttp://arxiv.org/abs/math-ph/0310016
dc.identifierJ. Stat. Phys. (2004) 116, pp. 1471-1490
dc.identifierdoi:10.1023/B:JOSS.0000041727.66775.d3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132196
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectNumber Theory
dc.subject11Z05, 82B26, 82B27, 82B28
dc.titleThermodynamics of the Farey Fraction Spin Chain
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