Dynamic universality class of Model C from the functional renormalization group

TL;DR

This paper uses the functional renormalization group to analyze the dynamic universality class of Model C, revealing new scaling behaviors, an anomalous diffusion phase, and an extended weak scaling region in dimensions 2 to 4.

Contribution

It introduces a nonperturbative analysis of Model C's dynamic critical behavior, uncovering new phases and scaling regimes in a broad dimensional range.

Findings

Identification of an anomalous diffusion phase

Extended weak scaling region in the phase diagram

Determination of scaling exponents and stability properties

Abstract

We establish new scaling properties for the universality class of Model C, which describes relaxational critical dynamics of a nonconserved order parameter coupled to a conserved scalar density. We find an anomalous diffusion phase, which satisfies weak dynamic scaling while the conserved density diffuses only asymptotically. The properties of the phase diagram for the dynamic critical behavior include a significantly extended weak scaling region, together with a strong and a decoupled scaling regime. These calculations are done directly in 2 < d < 4 space dimensions within the framework of the nonperturbative functional renormalization group. The scaling exponents characterizing the different phases are determined along with subleading indices featuring the stability properties.