70 citations · 121 across the 7 of their papers we have counts for
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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…
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…
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…
The Phase Transition in Statistical Models Defined on Farey Fractions
Jan Fiala, Peter Kleban, Ali Ozluk
We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as "spin chains", with long-range interactions, while another arises in t…