Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark

TL;DR

This paper develops frequency-dependent regulators for the nonperturbative renormalization group, demonstrating their necessity and effectiveness in accurately computing critical exponents in out-of-equilibrium systems like model A.

Contribution

It introduces a general framework for frequency regulators in the nonperturbative RG and shows their importance for consistent optimization of critical exponents.

Findings

Frequency regulators compatible with causality and fluctuation-dissipation theorem are feasible.

Using PMS, frequency regulators are essential for self-consistent critical exponent optimization.

Application to model A yields accurate dynamical critical exponent z.

Abstract

We derive the necessary conditions for implementing a regulator that depends on both momentum and frequency in the nonperturbative renormalization group flow equations of out-of-equilibrium statistical systems. We consider model A as a benchmark and compute its dynamical critical exponent $z$. This allows us to show that frequency regulators compatible with causality and the fluctuation-dissipation theorem can be devised. We show that when the Principle of Minimal Sensitivity (PMS) is employed to optimize the critical exponents $\eta$, $\nu$ and $z$, the use of frequency regulators becomes necessary to make the PMS a self-consistent criterion.