Renormalization, thermodynamic formalism and quasi-crystals in subshifts

DOI10.1007/s00220-012-1651-4zbMath1271.82017arXiv1010.4643OpenAlexW2009235939WikidataQ59184778 ScholiaQ59184778MaRDI QIDQ356679

Henk Bruin, Renaud Leplaideur

Publication date: 26 July 2013

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

Full work available at URL: https://arxiv.org/abs/1010.4643

zbMATH Keywords

phase transitionsCantor setFeigenbaum-Coullet-Tresser mapManneville-Pomeau maprenormalizable dynamical systemsThue-Morse substitution

Mathematics Subject Classification ID

Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Universality and renormalization of dynamical systems (37E20) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26) Renormalization of holomorphic dynamical systems (37F25)

Related Items (15)

About Phase Transition and Zero Temperature ⋮ Active particles in reactive disordered media: how does adsorption affect diffusion? ⋮ Typical ground states for large sets of interactions ⋮ Sensitive dependence of geometric Gibbs states at positive temperature ⋮ Persistent non-statistical dynamics in one-dimensional maps ⋮ Nonlinear thermodynamical formalism ⋮ A general renormalization procedure on the one-dimensional lattice and decay of correlations ⋮ Degenerated ground-states in a spin chain with pair interactions: a characterization by symbolic dynamics ⋮ Specification and towers in shift spaces ⋮ Thermodynamic formalism and \(k\)-Bonacci substitutions ⋮ Multiple phase transitions on compact symbolic systems ⋮ Phase transitions in one-dimensional translation invariant systems: a Ruelle operator approach ⋮ Sturmian ground states in classical lattice-gas models ⋮ Freezing phase transition in a fractal potential ⋮ An estimation of phase transition ^*

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ground states of two-dimensional Ising spin glasses: fast algorithms, recent developments and a ferromagnet-spin glass mixture
• Breaking of periodicity at positive temperatures
• New proofs of the existence of the Feigenbaum functions
• Some combinatorial properties of the Thue-Morse sequence and a problem in semigroups
• How should one define a (weak) crystal?
• Nonperiodic long-range order for fast-decaying interactions at positive temperatures
• Enumeration of factors in the Thue-Morse word
• Existence of a phase-transition in a one-dimensional Ising ferromagnet
• Statistical mechanics of a one-dimensional lattice gas
• On discontinuity of the pressure
• Ising model and Bernoulli schemes in one dimension
• Zero-temperature limit of one-dimensional Gibbs states via renormalization: the case of locally constant potentials
• Superimposed particles in 1D ground states
• THE POTENTIAL POINT OF VIEW FOR RENORMALIZATION
• Combinatorics on Words
• On t-conformal measures and Hausdorff dimension for a family of non-uniformly hyperbolic horseshoes
• DISORDERED GROUND STATES OF CLASSICAL LATTICE MODELS
• The spectrum of dynamical systems arising from substitutions of constant length
• Examples for the Nonuniqueness of the Equilibrium State
• ON THERMODYNAMICS OF RATIONAL MAPS. II: NON-RECURRENT MAPS
• Thermodynamic Formalism
• Local product structure for Equilibrium States
• Hausdorff dimension and conformal measures of Feigenbaum Julia sets
• 0-1-sequences of Toeplitz type
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness

This page was built for publication: Renormalization, thermodynamic formalism and quasi-crystals in subshifts