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

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 Z2-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.

Automated summary

This study employs Nishimori's gauge theory to investigate spontaneous symmetry breaking phenomena in the transverse field mixed p-spin glass model in finite dimensions. Useful identities in the gauge theory allow for the study of Z2-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 the absence of both ferromagnetic long-range order and spontaneous magnetization in the spin glass phase. It is also proven that the ferromagnetic susceptibility has an upper bound in the paramagnetic and spin glass phases.