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

Abstract

Spontaneous symmetry breaking phenomena in the transverse field mixed $p$-spin glass model in finite dimensions are studied with Nishimori's gauge theory. Useful identities in the gauge theory enable us to study ${\mathbb{Z}}_2$-symmetry breaking. It is proven that ferromagnetic long-range order and spontaneous magnetization at an arbitrary temperature are bounded by those on the Nishimori line in the corresponding classical model. These bounds imply that neither ferromagnetic long-range order nor spontaneous magnetization exists in spin glass phase. It is proven also that the ferromagnetic susceptibility has an upper bound in paramagnetic and spin glass phases.

9 pages. v2: Reference updated

References in corpus (4)

• Thermodynamics and Universality for Mean Field Quantum Spin Glasses
• Existence of replica-symmetry breaking in quantum glasses
• Gauge Theory for Quantum Spin Glasses
• Universality of replica-symmetry breaking in the transverse field Sherrington-Kirkpatrick model

Cited by in corpus (4)

• Anomalous distribution of magnetization in an Ising spin glass with correlated disorder
• Gauge theory for mixed $p$-spin glasses
• Gauge theory for quantum XYZ spin glasses
• Toward mean-field bound for critical temperature on Nishimori line