Gauge theory for mixed $p$-spin glasses

Abstract

Physical quantities in the mixed $p$-spin glasses are evaluated with Nishimori's gauge theory and several variance inequalities. The ${\mathbb{Z}}_2$-symmetry breaking and the replica-symmetry breaking 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 replica-symmetry breaking on the Nishimori line.

13 pages

References in corpus (6)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Absence of replica symmetry breaking in the random field Ising model
• Gauge Theory for Quantum Spin Glasses
• Non-linear PDEs approach to statistical mechanics of Dense Associative Memories
• Gibbs-Bogoliubov inequality on Nishimori line
• Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed $p$-spin Glass Models

Cited by in corpus (2)

• Gauge theory for quantum XYZ spin glasses
• Toward mean-field bound for critical temperature on Nishimori line