2024/08/05 by Lahoche, Vincent, Samary, Dine Ousmane, Radpay, Parham
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences
paper · doi:10.48550/arxiv.2408.02602
This paper examines the quantum (2+p)-spin dynamics of a N-vector x∈ ℝN 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=∞, and additional analytic material is given in the appendix.