Low temperature dynamics for confined $p=2$ soft spin in the quenched regime
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866912027297972224 |
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| author | Lahoche, Vincent Samary, Dine Ousmane |
| author_facet | Lahoche, Vincent Samary, Dine Ousmane |
| contents | 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 $a(t)\equiv \sum_i q_i^2(t)/N$ 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 reach this point dynamically. This allows to identify 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_07809 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Low temperature dynamics for confined $p=2$ soft spin in the quenched regime Lahoche, Vincent Samary, Dine Ousmane High Energy Physics - Theory 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 $a(t)\equiv \sum_i q_i^2(t)/N$ 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 reach this point dynamically. This allows to identify 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. |
| title | Low temperature dynamics for confined $p=2$ soft spin in the quenched regime |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2211.07809 |