Large time zero temperature dynamics of the spherical p = 2spin 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) spinglass 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 nearextreme eigenvalues at the edge of the spectrum of the coupling matrix $J$, and are thus non selfaveraging. 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.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 November 2015
 DOI:
 10.1088/17425468/2015/11/P11017
 arXiv:
 arXiv:1507.08520
 Bibcode:
 2015JSMTE..11..017F
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Mathematics  Probability
 EPrint:
 18 pages, 3 figures. Published version