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.

arXiv comment9 pages. v2: Reference updated

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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