Gauge theory for mixed p-spin glasses

Physical quantities in the mixed p-spin glasses are evaluated with Nishimori's gauge theory and several variance inequalities. The Z2-symmetry breaking and the replica-symmetry breaking (RSB) are studied in finite and infinite dimensions. Obtained bounds on the expectation of the square of the magnetization and spontaneous magnetization enable us to clarify properties of paramagnetic and spin glass phases. It is proven that variances of ferromagnetic and spin glass order parameters vanish on the Nishimori line in the infinite volume limit. These results imply the self-averaging of these order parameters on the Nishimori line. The self-averaging of the spin glass order parameter rigorously justifies already argued absence of RSB on the Nishimori line.

Automated summary

Physical quantities in the mixed p-spin glasses are evaluated using Nishimori's gauge theory and several variance inequalities. Z2-symmetry breaking and replica-symmetry breaking (RSB) are studied in both finite and infinite dimensions. Bounds on the expectation of the square of the magnetization and spontaneous magnetization clarify properties of the paramagnetic and spin glass phases. The study proves that variances of ferromagnetic and spin glass order parameters vanish on the Nishimori line in the infinite volume limit, suggesting self-averaging of these order parameters. This self-averaging of the spin glass order parameter justifies the absence of RSB on the Nishimori line.