# Large time effective kinetics $\\beta$-functions for quantum (2+p)-spin glass

Source: [Large time effective kinetics $\\beta$-functions for quantum (2+p)-spin glass](<https://www.sota2.com/research/paper/68fa4a8d1e209131ce93f517>)

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Data updated: 2026-02-05T05:00:14.183Z

Authors: Vincent Lahoche, Dine Ousmane Samary, Parham Radpay

Published: 2024-08-05T16:22:28.000Z

## Abstract

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 $\\beta$-functions. Our explicit calculations focus on the cases $p=3$, $p=\\infty$, and additional analytic material is given in the appendix.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2408.02602>)

[PDF](<https://arxiv.org/pdf/2408.02602.pdf>)