Spontaneous symmetry breaking in two dimensions under non-equilibrium laminar flows

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 the 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 between 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.