Large time zero temperature dynamics of the spherical p=2-spin glass model of finite size

Abstract

We revisit the long time dynamics of the spherical fully connected $p=2$-spin glass model when the number of spins $N$ is large but {\it finite}. At $T=0$ where the system is in a (trivial) spin-glass phase, and on long time scale $t\gtrsim \mathcal{O}(N^{2/3})$ we show that the behavior of physical observables, like the energy, correlation and response functions, is controlled by the density of near-extreme eigenvalues at the edge of the spectrum of the coupling matrix $J$, and are thus non self-averaging. We show that the late time decay of these observables, once averaged over the disorder, is controlled by new universal exponents which we compute exactly.

18 pages, 3 figures. Published version

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• Critical Behaviour of the Number of Minima of a Random Landscape at the Glass Transition Point and the Tracy-Widom distribution
• Density of near-extreme events
• Spherical model of growing interfaces
• Matrix optimization under random external fields
• The density of eigenvalues seen from the soft edge of random matrices in the Gaussian beta-ensembles

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