Renormalized field theory for the static crossover in isotropic dipolar ferromagnets

We present a field-theoretic description of the static crossover in ferromagnets with both short-range exchange and long-range dipolar interaction. In contrast to earlier approaches the calculations are carried out in terms of the natural reduced temperature variable r, relative to the dipolar critical temperature. The tensorial structure of the vertex functions, imposed by the presence of the dipolar interaction, leads to an anisotropic field renormalization and ultimately to the identification of new nonleading critical exponents for the longitudinal static susceptibility in two-loop order. Within this theoretical framework we are further able to investigate problems of universality. Especially we scrutinize the existence and the magnitude of the dip in the effective critical exponent ${\gamma }_{\mathrm{eff}}$(r) of the static transverse susceptibility found by matching techniques used in earlier studies.