- 03-277 Pierluigi Contucci, Sandro Graffi
- Convex Replica Simmetry Breaking from Positivity and Thermodynamic Limit
Jun 12, 03
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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.