Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed p-spin Glass Models

Article Physics, Mathematical

Universality of Replica-Symmetry Breaking in the Transverse Field Sherrington-Kirkpatrick Model

C. Itoi et al.

Summary: The existence theorem for replica-symmetry breaking in the transverse field Sherrington-Kirkpatrick model is extended to a model with general random exchange interactions. An approximate integration by parts is used to obtain the relation between the expectation value of the exchange interaction energy and the Duhamel correlation function of spin operators for general random interactions. In addition to the Falk-Bruch inequality, explicit evaluations are used to prove that the variance of overlap between two replica spin operators does not vanish under sufficiently weak transverse field in sufficiently low temperature. The absence of ferromagnetic long-range order is also shown to distinguish replica-symmetry breaking from Z(2)-symmetry breaking.

JOURNAL OF STATISTICAL PHYSICS (2023)

Add to Collection

Article Physics, Multidisciplinary

Existence of Replica-Symmetry Breaking in Quantum Glasses

Hajo Leschke et al.

Summary: By controlling quantum fluctuations with the Falk-Bruch inequality, a rigorous argument is provided for the possible existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick model at sufficiently low temperatures and fields. This argument also extends to the generalized model with multispin interactions, known as the transverse p-spin model.

PHYSICAL REVIEW LETTERS (2021)

Add to Collection

Article Physics, Mathematical