Critical aging and relaxation dynamics in long-range systems

We study the dynamical scaling of long-range 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 $σ$ 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.