Spontaneous symmetry breaking in two dimensions under nonequilibrium laminar flows

TL;DR

This paper investigates how different laminar flows affect long-range order in two-dimensional systems, revealing that shear and elongational flows stabilize order via superdiffusion, unlike rotational flow.

Contribution

It demonstrates the flow-dependent stability of long-range order in the $O(N)$ model, linking advective transport to superdiffusive behavior and order stabilization.

Findings

Shear and elongational flows stabilize long-range order.

Rotational flow does not stabilize long-range order.

Advective transport induces superdiffusion, stabilizing order.

Abstract

We study the long-range order in two dimensions where an order parameter is advected by laminar flows such as rotational, shear, and elongational flows. Under these flows, we analyze an ordered state of the $O(N)$ scalar model in the large-$N$ limit. We show that the stability of the ordered state depends on the flow pattern; shear and elongational flows stabilize the long-range order but rotational flow does not. We discuss the physical mechanism underlying our results by connecting static correlations of fluctuations and their dynamics based on the interaction representation used in quantum mechanics. We find that advective transport induces superdiffusion under shear and elongational flows, thereby stabilizing the long-range order.