The Ghirlanda-Guerra Identities

2005/05/20 by Pierluigi Contucci, Cristian Giardinà, Contucci, Pierluigi +2
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.dis-nn #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.math-ph/0505055

18 pages

arxiv created 2005/05/20 · openalex publication_date 2005/05/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.

Citations

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

Related

• The Ghirlanda-Guerra identities without averaging
• A new representation of the Ghirlanda-Guerra identities with applications
• The Parisi ultrametricity conjecture
• Self-Averaging Identities for Random Spin Systems
• Universality of Ghirlanda-Guerra identities and spin distributions in mixed p-spin models