Generalized Farey trees, transfer operators and phase transitions

DOI10.1007/s00220-007-0294-3zbMath1131.37040arXivmath-ph/0606020OpenAlexW2102545155MaRDI QIDQ2472482

Stefano Isola, Andreas Knauf, Mirko Degli Esposti

Publication date: 22 February 2008

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0606020

zbMATH Keywords

thermodynamic formalismdynamical binary trees and codingone-parameter family of 1D mapspolymer model analysis of the Markov family

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Phase transitions (general) in equilibrium statistical mechanics (82B26) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamical systems involving maps of the interval (37E05) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) General groups of measure-preserving transformations and dynamical systems (37A15)

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Cites Work

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• Maps of intervals with indifferent fixed points: thermodynamic formalism and phase transitions
• Intermittency and regularized Fredholm determinants
• The number-theoretical spin chain and the Riemann zeroes
• A one-parameter family of analytic Markov maps with an intermittency transition
• On a ferromagnetic spin chain
• Perturbation theory for linear operators.
• A Farey fraction spin chain
• The phase transition in statistical models defined on Farey fractions
• NUMBER THEORY, DYNAMICAL SYSTEMS AND STATISTICAL MECHANICS
• Is our mathematics natural? The case of equilibrium statistical mechanics
• Gaussian correlation inequalities for ferromagnets
• Free energy and correlations of the number-theoretical spin chain
• On a ferromagnetic spin chain. II. Thermodynamic limit
• The phase transition of the number-theoretical spin chain
• On the spectrum of Farey and Gauss maps
• Towards a complete determination of the spectrum of a transfer operator associated with intermittency