Exact Scaling of Spin-Wave Correlations in the 2DXYFerromagnet with Dipolar Forces

Long-range spin-wave correlation functions in the ordered phase of a 2D $\mathrm{XY}$ ferromagnet with 2D dipolar forces are governed by the 2D smectic $A$ Hamiltonian and possess exact scaling. The latter confirms from a different perspective the exact results obtained recently for the 2D smectic $A$. Exact scaling holds in the ordered phase of the 2D $\mathrm{XY}$ ferromagnet with 3D dipolar forces, with the dimension of the spatial anisotropy being ${\Delta }_x=\frac{4}{3}$ and the anomalous dimension of spin being ${\eta }_{\phi }=\frac{1}{6}$.