Field dependence of the susceptibility maximum temperature in ferromagnets

It is shown within the mean-field Landau’s theory that if a ferromagnet in the presence of a magnetic field can be in a phase in which the magnetization is parallel to the field, the susceptibility has a maximum at a point ${t=t}_h$ and under magnetic field (H) this point is shifted according to $H^{2/3}.$ This 2/3 power law is independent of a spin model. The prediction of Landau’s theory is examined on the one-dimensional quantum $S=1/2\mathrm{}$ anisotropic Heisenberg model by using a linear real-space renormalization group. It has been found that for a longitudinal field only in the isotropic Heisenberg model the shift of the susceptibility maximum can be fitted satisfactory to a power law with exponent close to 2/3. In other cases the deviation from a single power law seems to be clear. On the other hand, for the field perpendicular to the easy axis the fit to a power law is excellent but a value of the exponent depends on the anisotropy constant.