Convex Replica Simmetry Breaking From Positivity and Thermodynamic Limit

Abstract

Consider a correlated Gaussian random energy model built by successively adding one particle (spin) into the system and imposing the positivity of the associated covariance matrix. We show that the validity of a recently isolated condition ensuring the existence of the thermodynamic limit forces the covariance matrix to exhibit the Parisi replica symmetry breaking scheme with a convexity condition on the matrix elements.

11 pages

References in corpus (2)

• The Thermodynamic Limit in Mean Field Spin Glass Models
• Thermodynamical Limit for Correlated Gaussian Random Energy Models

Cited by in corpus (1)

• The Ghirlanda-Guerra Identities