70 citations · 121 across the 7 of their papers we have counts for
Showing 2005Show all
3 papers · 1 filter
cond-mat.stat-mech2005★ 12 cited
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★ 3 cited
Intervals Between Farey Fractions in the Limit of Infinite Level
Jan Fiala, Peter Kleban
The modified Farey sequence consists, at each level k, of rational fractions r_k^{(n)}, with n=1, 2, ...,2^k+1. We consider I_k^{(e)}, the total length of (one set of) alternate in…
math-ph2005★ 8 cited
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…