Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed <i>p</i>-spin Glass Models

Spontaneous symmetry breaking phenomena in the transverse field mixed $p$-spin glass model finite dimensions are studied with Nishimori's gauge theory. Useful identities 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 bounded by those on Nishimori line corresponding classical model. These bounds imply neither nor exists spin phase. also susceptibility has upper bound paramagnetic phases.