https://doi.org/10.1140/epjp/s13360-023-04039-5
Regular Article
Low-temperature dynamics for confined 
soft spin in the quenched regime
1
Université Paris Saclay, CEA List, 91191, Gif-sur-Yvette, France
2
International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, 072B.P.50, Cotonou, Republic of Benin
b
dine.ousmanesamary@cipma.uac.bj
Received:
18
February
2023
Accepted:
28
April
2023
Published online:
23
May
2023
This paper aims to address the low-temperature dynamics issue for the spin dynamics with confining potential, focusing especially on quartic and sextic cases. The dynamics are described by a Langevin equation for a real vector 
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 
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.
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