Large time effective kinetics $β$-functions for quantum (2+p)-spin glass
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912872365293568 |
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| author | Lahoche, Vincent Samary, Dine Ousmane Radpay, Parham |
| author_facet | Lahoche, Vincent Samary, Dine Ousmane Radpay, Parham |
| contents | This paper examines the quantum $(2+p)$-spin dynamics of a $N$-vector $\textbf{x}\in \mathbb{R}^N$ through the lens of renormalization group (RG) theory. The RG is based on a coarse-graining over the eigenvalues of matrix-like disorder, viewed as an effective kinetic whose eigenvalue distribution undergoes a deterministic law in the large $N$ limit. We focus our investigation on perturbation theory and vertex expansion for effective average action, which proves more amenable than standard nonperturbative approaches due to the distinct non-local temporal and replicative structures that emerge in the effective interactions following disorder integration. Our work entails the formulation of rules to address these non-localities within the framework of perturbation theory, culminating in the derivation of one-loop $β$-functions. Our explicit calculations focus on the cases $p=3$, $p=\infty$, and additional analytic material is given in the appendix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02602 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large time effective kinetics $β$-functions for quantum (2+p)-spin glass Lahoche, Vincent Samary, Dine Ousmane Radpay, Parham Disordered Systems and Neural Networks This paper examines the quantum $(2+p)$-spin dynamics of a $N$-vector $\textbf{x}\in \mathbb{R}^N$ through the lens of renormalization group (RG) theory. The RG is based on a coarse-graining over the eigenvalues of matrix-like disorder, viewed as an effective kinetic whose eigenvalue distribution undergoes a deterministic law in the large $N$ limit. We focus our investigation on perturbation theory and vertex expansion for effective average action, which proves more amenable than standard nonperturbative approaches due to the distinct non-local temporal and replicative structures that emerge in the effective interactions following disorder integration. Our work entails the formulation of rules to address these non-localities within the framework of perturbation theory, culminating in the derivation of one-loop $β$-functions. Our explicit calculations focus on the cases $p=3$, $p=\infty$, and additional analytic material is given in the appendix. |
| title | Large time effective kinetics $β$-functions for quantum (2+p)-spin glass |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2408.02602 |