[Submitted on 11 Apr 2025] (cross-list from hep-th)
Universality of relaxation dynamics for -symmetric spin-models
Duff Neill🇺🇸 · Hanqing Liu🇺🇸
Spin-models, where the spins interact pairwise with a symmetry preserving hamiltonian, famously simplify in the large , limits, as derived by Sachdev and Ye when exploring mean-field behavior of spin-glasses. We present numerical evidence that for a large class of models, the large limit is not necessary: the same dynamical equations can describe the relaxation processes at high temperatures for a set of classical models inspired from mean-field treatments of interacting dense neutrino gases, up to times set by the radius of convergence of the perturbation series for the correlation function. After a simple rescaling of time, the dynamics display a surprising universality, being identical for any value of as long as the rank of the coupling matrix is small. As a corollary of our results, we find that the direct interaction approximation originating from the study of stochastic flows in fluid turbulence should be thought of as only a short-time approximation for generic random coupling systems.
- Comments:
- LA-UR-25-20460
- Subjects:
- High Energy Physics — Theory (hep-th); cond-mat.dis-nn (cond-mat.dis-nn); Nuclear Theory (nucl-th); Fluid Dynamics (physics.flu-dyn)
- arXiv:
- 2504.08925 [pdf]