Model C critical dynamics of disordered magnets

TL;DR

This paper investigates the critical dynamics of disordered magnets within model C, employing renormalization group methods and advanced approximations to understand how disorder affects non-asymptotic critical behavior.

Contribution

It introduces a renormalization group procedure for disordered model C and demonstrates that two-loop approximation with resummation yields accurate critical dynamics predictions.

Findings

One-loop approximation captures qualitative behavior.

Two-loop approximation improves quantitative accuracy.

Resummation techniques are essential for reliable results.

Abstract

The critical dynamics of model C in the presence of disorder is considered. It is known that in the asymptotics a conserved secondary density decouples from the nonconserved order parameter for disordered systems. However couplings between order parameter and secondary density cause considerable effects on non-asymptotic critical properties. Here, a general procedure for a renormalization group treatment is proposed. Already the one-loop approximation gives a qualitatively correct picture of the diluted model C dynamical criticality. A more quantitative description is achieved using two-loop approximation. In order to get reliable results resummation technique has to be applied.