Absence of replica symmetry breaking in the transverse and longitudinal random field Ising model

Abstract

It is proved that replica symmetry is not broken in the transverse and longitudinal random field Ising model. In this model, the variance of spin overlap of any component vanishes in any dimension almost everywhere in the coupling constant space in the infinite volume limit. The weak Fortuin-Kasteleyn-Ginibre property in this model and the Ghirlanda-Guerra identities in artificial models in a path integral representation based on the Lie-Trotter-Suzuki formula enable us to extend Chatterjee's proof for the random field Ising model to the quantum model.

17 pages, to appear in J. Stat. Phys

References in corpus (4)

• Absence of replica symmetry breaking in the random field Ising model
• Thermodynamics and Universality for Mean Field Quantum Spin Glasses
• Universal nature of replica symmetry breaking in quantum systems with Gaussian disorder
• General properties of overlap operators in disordered quantum spin systems

Cited by in corpus (5)

• No replica symmetry breaking phase in random field Ginzburg-Landau model
• Zero-variance of perturbation Hamiltonian density in perturbed spin systems
• Absence of replica symmetry breaking in disordered FKG-Ising models under uniform field
• Absence of Replica Symmetry Breaking in Finite Fifth Moment Random Field Ising Model
• The Schwartz-Soffer and more inequalities for random fields