Magnetization and magnetic entropy change of a three-dimensional isotropic ferromagnet near the Curie temperature in the random phase approximation

The behavior of a three-dimensional isotropic Heisenberg ferromagnet in the presence of a magnetic field H is investigated in the random phase approximation (RPA) near the Curie temperature Tc. It is shown that the magnetization M at the Curie temperature Tc is described by the law M(T=Tc)∼H1/5 and the initial magnetic susceptibility χ0 at temperatures T≥Tc is given by χ0(T≥Tc)∼(T−Tc)−2. It means that in the RPA the critical exponents for a three-dimensional Heisenberg ferromagnet coincide with the critical exponents for the Berlin-Kac spherical model of a ferromagnet rather than with the critical exponents of the mean field approximation (MFA). Hence it follows as well that, when a magnetic field H is risen from H=0 to H=Ha, the magnetic entropy SM will be decreased as ΔSM(T=Tc)∼−Ha4/5 at the Curie temperature Tc and as ΔSM(T>Tc)∼−(T−Tc)−3Ha2 at temperatures T>Tc.