2024/12/23 by Lahoche, Vincent, Samary, Dine Ousmane, Radpay, Parham
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2412.17600
To gain a deeper understanding of the glassy phase in p-spin quantum models, this paper examines the dynamics of the N-vector \bmx ∈ ℝN through the framework of renormalization group theory. First, we focus on perturbation theory, which is more suitable than nonperturbative techniques due to the specific temporal non-locality of the model after disorder integration. We compute the one-loop β-function and explore the structure of its fixed points. Next, we develop the nonperturbative renormalization group approach based on the standard Wetterich-Morris formalism, using two approximation schemes to address the model's non-locality. We investigate the vertex expansion in the symmetric phase and assess the reliability of the approximations for the fixed-point solutions. Finally, we extend our analysis beyond the symmetric phase by using an expansion around the vacuum of the local potential. Our numerical investigations particularly focus on the cases p = 2 and p=3.