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Critical aging and relaxation dynamics in long-range systems

Valerio Pagni1,*, Friederike Ihssen2, and Nicolò Defenu1

  • *Contact author: vpagni@phys.ethz.ch
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Phys. Rev. Research 8, 043144 – Published 9 November, 2026

DOI: https://doi.org/10.1103/31g2-slsh

Abstract

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.

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Phys. Rev. Research 8, 043144– Published 9 November, 2026
  • Received 7 January 2026
  • Accepted 14 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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