Critical dynamics in a real-time formulation of the functional renormalization group

TL;DR

This paper develops a real-time functional renormalization group approach to compute critical spectral functions and dynamic critical exponents for Models A, B, and C, providing new insights into their critical dynamics.

Contribution

It introduces a real-time FRG framework with 1-loop and 2-loop schemes to analyze critical spectral functions and dynamics of Models A, B, and C, including the coupling effects predicted by Son and Stephanov.

Findings

Calculated critical spectral functions for Models A, B, and C.

Extracted dynamic critical exponents in 2D and 3D.

Compared results with existing literature, confirming theoretical predictions.

Abstract

We present first calculations of critical spectral functions of the relaxational Models A, B, and C in the Halperin-Hohenberg classification using a real-time formulation of the functional renormalization group (FRG). We revisit the prediction by Son and Stephanov that the linear coupling of a conserved density to the non-conserved order parameter of Model A gives rise to critical Model-B dynamics. We formulate both 1-loop and 2-loop self-consistent expansion schemes in the 1PI vertex functions as truncations of the effective average action suitable for real-time applications, and analyze in detail how the different critical dynamics are properly incorporated in the framework of the FRG on the closed-time path. We present results for the corresponding critical spectral functions, extract the dynamic critical exponents for Models A, B, and C, in two and three spatial dimensions, respectively, and compare the resulting values with recent results from the literature.