Non-local conservation in the coupling field: effect on critical dynamics

TL;DR

This paper investigates how long-range diffusion affects the critical dynamics of a coupled non-conserved and conserved field system, revealing different regimes with varying dynamic exponents through renormalization group analysis.

Contribution

It introduces a comprehensive analysis of critical dynamics with long-range conservation, identifying distinct regimes and their dependence on the transport exponent and number of components.

Findings

Identifies three regimes with different dynamic exponents in the long-range conserved system.

Shows the known local conservation case is a special limit within these regimes.

Provides renormalization group calculations up to one loop order for the model.

Abstract

We consider the critical dynamics of a system with an $n$-component non-conserved order parameter coupled to a conserved field with long range diffusion. An exponent $\sigma$ characterizes the long range transport, $\sigma=2$ being the known locally conserved case. With renormalisation group calculations done upto one loop order, several regions are found with different values of the dynamic exponent $z$ in the $\sigma -n$ plane. For $n<4$, there are three regimes, I: nonuniversal, $\sigma$ dependent $z$, II: universal with $z$ depending on $n$ and III': conservation law irrelevant, $z$ being equal to that in the nonconserved case. The known locally conserved case belongs to regions I and II.