We use the Renormalization Group method to study the Bose-Einstein
condensation of the interacting dilute magnons which appears in three
dimensional spin systems in magnetic field. The obtained temperature dependence
of the critical field Hcβ(T)βHcβ(0)βΌT2 is different from the recent
self-consistent Hartree-Fock-Popov calculations (cond-mat/0405422) in which a
T3/2 dependence was reported . The origin of this difference is discussed
in the framework of quantum critical phenomena.Comment: 11 pages, revtex