Critical aging and relaxation dynamics in long-range systems

TL;DR

This paper investigates the aging and relaxation dynamics of long-range $ ext{O}(N)$ models at criticality using the functional renormalization group, revealing improved predictions over perturbative methods and implications for heat engine performance.

Contribution

It introduces a non-perturbative analysis of aging and relaxation in long-range systems, extending understanding beyond previous perturbative approaches.

Findings

Enhanced accuracy over perturbative predictions

Demonstrated impact of interaction range on dynamics

Showed potential for improved heat engine efficiency

Abstract

We study the dynamical scaling of long-range $\mathrm{O}(N)$ models after a sudden quench to the critical temperature, using the functional renormalization group approach. We characterize both short-time aging and long-time relaxation as a function of the symmetry index $N$, the interaction range decay exponent $\sigma$ and the dimension $d$. Our results substantially improve on perturbative predictions, as demonstrated by benchmarks against Monte Carlo simulations and the large-$N$ limit. Finally, we demonstrate that long-range systems increase the performance of critical heat engines with respect to a local active medium.