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.

arXiv comment11 pages. To appear in Commun. Math. Phys

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• Universal nature of replica symmetry breaking in quantum systems with Gaussian disorder
• General properties of overlap operators in disordered quantum spin systems
• An improved Belief Propagation algorithm finds many Bethe states in the random field Ising model on random graphs
• Concentration of multi-overlaps for random ferromagnetic spin models
• The Effect of Defects on Magnetic Droplet Nucleation
• Proof of single-replica equivalence in short-range spin glasses
• Self-averaging of perturbation Hamiltonian density in perturbed spin systems
• The Ising spin glass on random graphs at zero temperature: not all spins are glassy in the glassy phase
• Absence of replica symmetry breaking in the transverse and longitudinal random field Ising model
• The Sherrington-Kirkpatrick model for spin glasses: A new approach for the solution
• No replica symmetry breaking phase in random field Ginzburg-Landau model
• Gauge theory for mixed $p$-spin glasses
• Zero-variance of perturbation Hamiltonian density in perturbed spin systems
• Absence of replica symmetry breaking in disordered FKG-Ising models under uniform field
• Uniqueness of ground state in the Edwards-Anderson spin glass model
• Universality of chaos and ultrametricity in mixed p-spin models
• On the Ultrametricity Property in Random Field Ising Models
• The Schwartz-Soffer and more inequalities for random fields
• Absence of replica symmetry breaking in the Edwards-Anderson model near zero temperature
• Proof of avoidability of the quantum first-order transition in transverse magnetization in quantum annealing of finite-dimensional spin glasses
• Griffiths-type theorems for short-range spin glass models
• Absence of Replica Symmetry Breaking in the Random Field Mixed-Spin Ginzburg-Landau Model
• Some examples of quenched self-averaging in models with Gaussian disorder