Scaling behaviour of non-equilibrium planar N-atic spin systems under weak fluctuations

Abstract

Starting from symmetry considerations, we derive the generic hydrodynamic equation of non-equilibrium XY spin systems with N-atic symmetry under weak fluctuations. Through a systematic treatment we demonstrate that, in two dimensions, these systems exhibit two types of scaling behaviours. For N = 1, they have long-range order and are described by the flocking phase of dry polar active fluids. For all other values of N, the systems exhibit quasi long-range order, as in the equilibrium XY model at low temperature.