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

Yan V. Fyodorov 1 Anthony Perret 2 Gregory Schehr 2

Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2015, pp.P11017

We revisit the long time dynamics of the spherical fully connected spin-glass model, i.e. the spherical $p=2$-spin model, when the number of spins $N$ is large but finite. At $T=0$ where the system is in a (trivial) spin-glass phase, and on long time scale $t \gtrsim {\cal O}{(N^{2/3})}$ 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.

  • 1. School of Mathematical Sciences [London]
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques