Entropic Repulsion and Lack of the g-Measure Property for Dyson Models

Author(s)

Bissacot, Rodrigo ^[1] ; Endo, Eric O. ^{[2, 1]} ; van Enter, Aernout C. D. ^[2] ; Le Ny, Arnaud ^[3]

Affiliation

^[1] Univ Sao Paulo, IME, Inst Math & Stat, Sao Paulo - Brazil

^[2] Univ Groningen, Johann Bernoulli Inst Math & Comp Sci, Groningen - Netherlands

^[3] Univ Paris Est UPEC, CNRS, UMR 8050, Lab Math & Anal Appl, LAMA, Creteil - France

• Document type: Journal article
• Source: Communications in Mathematical Physics; v. 363, n. 3, p. 767-788, NOV 2018.
• Web of Science Citations: 1

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. (AU)

• FAPESP's process: 15/14434-8 - Phase Transitions in Spin Models with General External Fields
• Grantee: Eric Ossami Endo
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 16/25053-8 - Dynamics and geometry in low dimensions
• Grantee: André Salles de Carvalho
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 14/10637-9 - Combinatorial Problems in Ferromagnetic Models
• Grantee: Eric Ossami Endo
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 16/08518-7 - Gibbs Measures and Phase Transitions
• Grantee: Rodrigo Bissacot Proença
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 11/16265-8 - Low dimensional dynamics
• Grantee: Edson Vargas
• Support Opportunities: Research Projects - Thematic Grants