3 papers
cond-mat.stat-mech2005
Cluster Approximation for the Farey Fraction Spin Chain
T. Prellberg, J. Fiala, P. Kleban
We consider the Farey fraction spin chain in an external field . Utilising ideas from dynamical systems, the free energy of the model is derived by means of an effective cluster…
math-ph2005
Generalized Number Theoretic Spin Chain-Connections to Dynamical Systems and Expectation Values
Jan Fiala, Peter Kleban
We generalize the number theoretic spin chain, a one-dimensional statistical model based on the Farey fractions, by introducing a new parameter x>=0. This allows us to write recurs…
math-ph2003
Thermodynamics of the Farey Fraction Spin Chain
Jan Fiala, Peter Kleban
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 m…