Low-temperature dynamics for confined p=2 soft spin in the quenched regime.

This paper aims to address the low-temperature dynamics issue for the p = 2 spin dynamics with confining potential, focusing especially on quartic and sextic cases. The dynamics are described by a Langevin equation for a real vector q i of size N, where disorder is materialized by a Wigner matrix and we especially investigate the self-consistent evolution equation for effective potential arising from self-averaging of the square length a (t) ≡ ∑ i q i 2 (t) / N for large N. We first focus on the static case, assuming the system reached some equilibrium point, and we then investigate the way the system reaches this point dynamically. This allows identifying a critical temperature, above which the relaxation toward equilibrium follows an exponential law but below which it has infinite time life and corresponds to a power law decay. [ABSTRACT FROM AUTHOR]