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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.08925 |
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| _version_ | 1866912322130280448 |
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| author | Neill, Duff Liu, Hanqing |
| author_facet | Neill, Duff Liu, Hanqing |
| contents | Spin-models, where the $N$ spins interact pairwise with a $SU(n_f)$ symmetry preserving hamiltonian, famously simplify in the large $n_f$, $N$ 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 $n_f$ 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 $n_f$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08925 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality of $SU(\infty)$ relaxation dynamics for $SU(n_f)$-symmetric spin-models Neill, Duff Liu, Hanqing High Energy Physics - Theory Disordered Systems and Neural Networks Nuclear Theory Fluid Dynamics Spin-models, where the $N$ spins interact pairwise with a $SU(n_f)$ symmetry preserving hamiltonian, famously simplify in the large $n_f$, $N$ 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 $n_f$ 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 $n_f$ 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. |
| title | Universality of $SU(\infty)$ relaxation dynamics for $SU(n_f)$-symmetric spin-models |
| topic | High Energy Physics - Theory Disordered Systems and Neural Networks Nuclear Theory Fluid Dynamics |
| url | https://arxiv.org/abs/2504.08925 |