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29 March 2024
 
  » arxiv » cond-mat/9907296

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Index Distribution of Random Matrices with an Application to Disordered Systems
Andrea Cavagna ; Juan P. Garrahan ; Irene Giardina ;
Date 20 Jul 1999
Journal Phys. Rev. B 61, 3960 (2000)
Subject Statistical Mechanics; Disordered Systems and Neural Networks | cond-mat.stat-mech cond-mat.dis-nn
AbstractWe compute the distribution of the number of negative eigenvalues (the index) for an ensemble of Gaussian random matrices, by means of the replica method. This calculation has important applications in the context of statistical mechanics of disordered systems, where the second derivative of the potential energy (the Hessian) is a random matrix whose negative eigenvalues measure the degree of instability of the energy surface. An analysis of the probability distribution of the Hessian index is therefore relevant for a geometric characterization of the energy landscape in disordered systems. The approach we use here is particularly suitable for this purpose, since it addresses the problem without any a priori assumption on the random matrix ensemble and can be naturally extended to more realistic, non-Gaussian distributions.
Source arXiv, cond-mat/9907296
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