Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-07-20
Phys. Rev. B 61, 3960 (2000)
Physics
Condensed Matter
Statistical Mechanics
16 pages, RevTeX, 3 EPS figures
Scientific paper
10.1103/PhysRevB.61.3960
We 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.
Cavagna Andrea
Garrahan Juan P.
Giardina Irene
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