Thermodynamics of the Farey Fraction Spin Chain
Mathematical Physics
2007-06-22 v2 Statistical Mechanics
math.MP
Number Theory
Abstract
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 . 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.
Keywords
Cite
@article{arxiv.math-ph/0310016,
title = {Thermodynamics of the Farey Fraction Spin Chain},
author = {Jan Fiala and Peter Kleban},
journal= {arXiv preprint arXiv:math-ph/0310016},
year = {2007}
}
Comments
20 pages, 5 figures, revtex4, proof completed in section III, added appendix and 2 references; accepted by Journal of Statistical Physics