Entropic repulsion and lack of the $g$-measure property for Dyson models

Abstract

We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not $g$-measures. The main ingredient in the proof is the occurrence of an entropic repulsion effect, which follows from the mesoscopic stability of a (single-point) interface for these long-range models in the phase transition region.

arXiv comment22 pages, 4 figures

References in corpus (8)

• Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
• Geometry of contours and Peierls estimates in d=1 Ising models
• Phase Transition in the 1d Random Field ising model with long range interaction
• Unique Bernoulli g-measures
• Phase Transitions in One-dimensional Translation Invariant Systems: a Ruelle Operator Approach
• Phase separation for the long range one--dimensional ising model
• On non-regular g-measures
• Contour methods for long-range Ising models: weakening nearest-neighbor interactions and adding decaying fields

Cited by in corpus (10)

• On concentration inequalities and their applications for Gibbs measures in lattice systems
• Non-regular g-measures and variable length memory chains
• Contour methods for long-range Ising models: weakening nearest-neighbor interactions and adding decaying fields
• Infinite DLR Measures and Volume-Type Phase Transitions on Countable Markov Shifts
• Large deviations of return times and related entropy estimators on shift spaces
• Decimations for Two-dimensional Ising and Rotator Models I
• Dynamical Gibbs-non-Gibbs transitions in the Curie-Weiss Potts model in the regime beta<3
• Thermodynamic formalism for amenable groups and countable state spaces
• The Eigenfunctions of the Transfer Operator for the Dyson model in a field
• Multifractal Formalism from Large Deviations