The limit distribution of a number theoretic function arising from a problem in statistical mechanics

DOI10.1006/JNTH.2001.2666zbMath1002.11072OpenAlexW1979343536MaRDI QIDQ5950939

Manfred Peter

Publication date: 2 January 2002

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.2001.2666

zbMATH Keywords

spin chainabsolutely continuous limit distributionarithmetical functionnonexistence of a limit

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Miscellaneous applications of number theory (11Z05) Distribution functions associated with additive and positive multiplicative functions (11N60)

Related Items (8)

Remark on the Farey fraction spin chain ⋮ Positive limit-Fourier transform of Farey fractions ⋮ Asymptotics of the Farey fraction spin chain free energy at the critical point ⋮ A mean value theorem for closed geodesics on congruence surfaces ⋮ Generalized number theoretic spin chain-connections to dynamical systems and expectation values ⋮ A thermodynamic classification of real numbers ⋮ Cluster approximation for the Farey fraction spin chain ⋮ Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals

Cites Work

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• On the distribution of the number of lattice points inside a family of convex ovals
• Almost periodicity of the normalized representation numbers associated to positive definite ternary quadratic forms
• A Farey fraction spin chain
• Distribution of the error term for the number of lattice points inside a shifted circle
• Moments of class numbers. III
• On the distribution of the values of quadratic L-series in the half-plane \(\sigma > 1/2\)
• Momente der Klassenzahlen binärer quadratischer Formen mit ganzalgebraischen Koeffizienten
• Class numbers of indefinite binary quadratic forms
• On asymptotic properties of a number theoretic function arising out of a spin chain model in statistical mechanics

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