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.

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

References in corpus (23)

• Exact evolution equation for the effective potential
• The nonperturbative functional renormalization group and its applications
• Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics
• Long-range interacting quantum systems
• Aging, rejuvenation and memory : the example of spin glasses
• Nonthermal fixed points and the functional renormalization group
• Critical exponents of O(N) models in fractional dimensions
• Non-perturbative Approach to Critical Dynamics
• Universality in driven open quantum matter
• Scaling Solutions in Continuous Dimension
• Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark
• Spectral functions and dynamic critical behavior of relativistic $Z_2$ theories
• Universal phenomenology at critical exceptional points of nonequilibrium $O(N)$ models
• Universality class of Ising critical states with long-range losses
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
• Nonequilibrium Criticality at the Onset of Time-Crystalline Order
• Real-time dynamics of the $O(4)$ scalar theory within the fRG approach
• Renormalization-group description of nonequilibrium critical short-time relaxation processes: a three-loop approximation
• Critical dynamics of relativistic diffusion
• Dissipation dynamics of a scalar field
• Stable and unstable perturbations in universal scaling phenomena far from equilibrium
• Collective non-equilibrium dynamics at surfaces and the spatio-temporal edge

Cited by in corpus (2)

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