Absence of replica symmetry breaking in the random field Ising model

Abstract

It is shown that replica symmetry is not broken in the random field Ising model in any dimension, at any temperature and field strength, except possibly at a measure-zero set of exceptional temperatures and field strengths.

11 pages. To appear in Commun. Math. Phys

References in corpus (2)

• No spin glass phase in ferromagnetic random-field random-temperature scalar Ginzburg-Landau model
• The physical Meaning of Replica Symmetry Breaking

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• The Ising spin glass on random graphs at zero temperature: not all spins are glassy in the glassy phase
• The Sherrington-Kirkpatrick model for spin glasses: A new approach for the solution
• Gauge theory for mixed $p$-spin glasses
• Uniqueness of ground state in the Edwards-Anderson spin glass model
• Universality of chaos and ultrametricity in mixed p-spin models
• Absence of Replica Symmetry Breaking in the Random Field Mixed-Spin Ginzburg-Landau Model
• Proof of avoidability of the quantum first-order transition in transverse magnetization in quantum annealing of finite-dimensional spin glasses
• Absence of replica symmetry breaking in the Edwards-Anderson model near zero temperature
• Griffiths-type theorems for short-range spin glass models