Field-induced Bose-Einstein condensation of interacting dilute magnons in three-dimensional spin systems: A renormalization-group study

We use the renormalization-group method to study the magnetic field influence on the Bose-Einstein condensation of interacting dilute magnons in three-dimensional spin systems. We first considered a model with SU(2) symmetry (universality class z=1) and we obtain for the critical magnetic field a power law dependence on the critical temperature, [H-c(T)-H-c(0)]similar to T-2. In the case of U(1) symmetry (universality class z=2) the dependence is different, and the magnetic critical field depends linearly on the critical temperature, [H-c(T)-H-c(0)]similar to T. By considering a more relevant model, which includes also the system's anisotropy, we obtain for the same symmetry class a T-3/2 dependence of the magnetic critical field on the critical temperature. We discuss these theoretical predictions of the renormalization group in connection with experimental results reported in the literature.