Long-range phase order in two dimensions under shear flow

TL;DR

This paper demonstrates that shear flow induces long-range phase order in a two-dimensional O(2) model, revealing a second-order phase transition with mean-field critical exponents under non-equilibrium conditions.

Contribution

It provides a theoretical and numerical analysis showing shear flow can stabilize long-range order in 2D systems, which is typically forbidden by the Mermin-Wagner theorem.

Findings

Shear flow suppresses phase fluctuations, enabling long-range order in 2D.

The phase transition is second order, with critical exponents close to mean-field values.

Long-range order persists under shear flow, contrary to equilibrium expectations.

Abstract

We theoretically and numerically investigate a two-dimensional O(2) model where an order parameter is convected by shear flow. We show that a long-range phase order emerges in two dimensions as a result of anomalous suppression of phase fluctuations by the shear flow. Furthermore, we use the finite-size scaling theory to demonstrate that a phase transition to the long-range ordered state from the disordered state is second order. At a transition point far from equilibrium, the critical exponents turn out to be close to the mean-field value for equilibrium systems.