Emergence of surface long-range order under uniform shear flow

TL;DR

This paper demonstrates that uniform shear flow can induce long-range order on a two-dimensional surface in a non-equilibrium steady state, overcoming thermal fluctuations that prevent such order at equilibrium.

Contribution

The study reveals how shear flow suppresses surface fluctuations, enabling long-range order in a 2D surface, analyzed exactly in the large-N limit.

Findings

Shear flow enhances surface correlations.

Long-range order emerges due to fluctuation suppression.

Exact large-N analysis confirms the phenomenon.

Abstract

We study the two-dimensional surface long-range order in a non-equilibrium steady state under shear flow using the three-dimensional conserved $O(N)$ model. Whereas the correlation on the surface is enhanced by increasing interactions within the surface, the long-range order cannot be realized at equilibrium because of divergent thermal fluctuations associated with the low dimensionality of the surface. Here, the shear flow is applied parallel to the surface, on which the flow is set to zero. Despite the shear flow not affecting the order parameter on the surface directly, the fluctuations at the surface are strongly suppressed by the flow away from the surface, leading to the surface long-range order. We demonstrate these results through an exact analysis in the large-$N$ limit, where non-linear fluctuations are self-consistently treated.