Hydrodynamic relation in 2D Heisenberg antiferromagnet in a field

The spin-stiffness \rho_s of a 2D Heisenberg antiferromagnet depends non-analytically on external magnetic field. We demonstrate that the hydrodynamic relation between \rho_s, the uniform susceptibility \chi, and the spin-wave velocity $c$ is not violated by such a behavior because similar non-analytic terms from all three quantities mutually cancel out. In this work, explicit expressions for the field-dependent spin stiffness and for the magnon velocity of the 2D square lattice antiferromagnet are obtained by direct calculation to order 1/S and in the whole range of magnetic fields.