Hydrodynamic relation in a two-dimensional Heisenberg antiferromagnet in a field

The spin stiffness rho(s) of a two-dimensional (2D) Heisenberg antiferromagnet depends nonanalytically 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 nonanalytic 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.