Convex Replica Simmetry Breaking From Positivity and Thermodynamic Limit
Disordered Systems and Neural Networks
2009-11-10 v1 Statistical Mechanics
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.cond-mat/0306326,
title = {Convex Replica Simmetry Breaking From Positivity and Thermodynamic Limit},
author = {Pierluigi Contucci and Sandro Graffi},
journal= {arXiv preprint arXiv:cond-mat/0306326},
year = {2009}
}
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11 pages