Phase transitions in ferromagnets with dipolar interactions and uniaxial anisotropy

Abstract

A renormalized-field theory for the critical behavior of ferromagnets with dipolar interactions and uniaxial anisotropy is developed to the one-loop order whereby the (reduced) dipolar g and uniaxial m couplings are studied on equal footing. A generalized minimal subtraction scheme is used to study the attractors and the renormalized flow of the ${\mathrm{\ensuremath{\varphi}}}^{4}$ coupling constant and, subsequently, to determine the Kouvel-Fisher effective exponent ${\ensuremath{\gamma}}_{\mathit{e}\mathit{f}\mathit{f}}$ for the longitudinal susceptibility for arbitrary values of m and g. Despite the difficulties brought about by the generality of treatment, the investigation was carried out analytically throughout. The crossover transitions between the four nontrivial fixed points (Heisenberg, Ising, uniaxial dipolar, and isotropic dipolar), as exemplified by ${\ensuremath{\gamma}}_{\mathit{e}\mathit{f}\mathit{f}}$, are determined in detail to the one-loop order of the theory. In particular, all previous predictions concerning the discussed features of criticality in dipolar ferromagnets are obtained as specific cases of the present study. The problems arising in an attempt to fix the physical scale in a renormalized-field theoretical treatment of crossover behavior are discussed in view of finding a qualitative interpretation of recent experimental results on Gd and ${\mathrm{Fe}}_{14}$${\mathrm{Nd}}_{2}$B.