Gauge theory for quantum XYZ spin glasses

Abstract

Nishimori's gauge theory is extended to the quantum XYZ $p$-spin glass model in finite dimensions. This enables us to obtain useful correlation equalities, which show also that Duhamel correlation functions at an arbitrary temperature are bounded by those in the corresponding classical model on the Nishimori line. These bounds give that the spontaneous magnetization vanishes in any low temperature even if the model enters the ${\mathbb{Z}}_2$-symmetry broken spin glass phase. This theory explains well-known fact from experiments and numerical calculations that the magnetic susceptibility does not diverge in the spin glass transition. The new gauge theory together with the known phase diagram of the Edwards-Anderson model can specify the spin glass region in the coupling constant space of the quantum Heisenberg XYZ spin glass model.

13 pages, 1 figure. arXiv admin note: text overlap with arXiv:2305.19630

References in corpus (8)

• Thermodynamics and Universality for Mean Field Quantum Spin Glasses
• Existence of replica-symmetry breaking in quantum glasses
• Gauge Theory for Quantum Spin Glasses
• Gibbs-Bogoliubov inequality on Nishimori line
• Mean-field theory is exact for Ising spin glass models with Kac potential in non-additive limit on Nishimori line
• Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed $p$-spin Glass Models
• Gauge theory for mixed $p$-spin glasses
• Universality of replica-symmetry breaking in the transverse field Sherrington-Kirkpatrick model

Cited by in corpus (1)

• Anomalous distribution of magnetization in an Ising spin glass with correlated disorder