Universal nature of replica symmetry breaking in quantum systems with Gaussian disorder

Abstract

We study quantum spin systems with quenched Gaussian disorder. We prove that the variance of all physical quantities in a certain class vanishes in the infinite volume limit. We study also replica symmetry breaking phenomena, where the variance of an overlap operator in the other class does not vanish in the replica symmetric Gibbs state. On the other hand, it vanishes in a spontaneous replica symmetry breaking Gibbs state defined by applying an infinitesimal replica symmetry breaking field. We prove also that the finite variance of the overlap operator in the replica symmetric Gibbs state implies the existence of a spontaneous replica symmetry breaking.

19 pages

References in corpus (4)

• Absence of replica symmetry breaking in the random field Ising model
• Thermodynamics and Universality for Mean Field Quantum Spin Glasses
• General properties of overlap operators in disordered quantum spin systems
• Non-differentiability of the effective potential and the replica symmetry breaking in the random energy model

Cited by in corpus (7)

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• Absence of replica symmetry breaking in the transverse and longitudinal random field Ising model
• Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed $p$-spin Glass Models
• 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
• Gauge theory for quantum XYZ spin glasses