Nonperturbative treatment of a quenched Langevin field theory

Abstract

We present a novel approach within the functional renormalization group framework for computing critical exponents that characterize the time evolution of out-of-equilibrium many-body systems. Our approach permits access to quantities involved in the renormalization procedure, using an expansion about time-translation invariant problems. This expansion can be upgraded to a fully time-dependent computation by iteration. As a prototypical example, we compute the aging exponent $\theta$ describing the dynamics of model A following a sudden quench to the critical point. Already at leading order, the approach demonstrates remarkable accuracy when compared with MC simulations and resummed perturbative expansions in the range $2<d<4$. This yields results that surpass those of the two-loop $\epsilon$ expansion in accuracy and match analytically known benchmarks at large $N$. These findings contribute to a deeper understanding of out-of-equilibrium universality and open new avenues for non-perturbative studies of critical dynamics, as well as for exploring the critical behavior of systems with spatial boundaries.

arXiv comment14 pages, 3 figures: Published in Phys. Rev. B in 112, 024306 (2025), Editor's Suggestion

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Cited by in corpus (2)

• Short-time dynamics in phase-ordering kinetics
• One-dimensional long-range Ising model: two (almost) equivalent approximations