Equality of the critical inverse temperatures for the one- and two-sided Dyson models

2025/12/19 by Berger, Noam, Johansson, Anders, Öberg, Anders
#37A60 #37D35 (Primary) #82B20 #82B26 #82C27 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2512.17451

Abstract

We prove that the critical inverse temperatures β_c^{\mathbb N}(α) and β_c^{\mathbb Z}(α) for the one- and two-sided Dyson models are the same when the power of the interaction strength α satisfies 1<α<2. We conjecture that this is true also in the remaining case of α=2.

Citations

• Concentration inequalities and Transfer operators for supercritical Dyson models
• On an extension of a theorem by Ruelle to long-range potentials
• The Eigenfunctions of the Transfer Operator for the Dyson model in a field
• Continuous eigenfunctions of the transfer operator for Dyson models
• Sharp phase transition for the random-cluster and Potts models via decision trees
• Phase transitions in long-range Ising models and an optimal condition for factors of g-measures
• The Random-Cluster Model

Related

• Thermodynamic limit of the first Lee-Yang zero
• BCS Critical Temperature on Half-Spaces
• Critical phenomena in the Dyson hierarchical model and renormalization group
• Critical Equalities for Potts Models
• ηandη′mesons in the Dyson-Schwinger approach at finite temperature