Thermodynamics of the Farey Fraction Spin Chain

Details Thermodynamics of the Farey Fraction Spin Chain Thermodynamics of the Farey Fraction Spin Chain

2003-10-09

arxiv.org/abs/math-ph/0310016v2

J. Stat. Phys. (2004) 116, pp. 1471-1490

Physics

Mathematical Physics

20 pages, 5 figures, revtex4, proof completed in section III, added appendix and 2 references; accepted by Journal of Statisti

Scientific paper

10.1023/B:JOSS.0000041727.66775.

We 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.

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