Renormalized Field Theory for the Static Crossover in Dipolar Ferromagnets

A field theoretical description for the static crossover in dipolar ferromagnets is presented. New non leading critical exponents for the longitudinal static susceptibility are identified and the existence and magnitude of the dip in the effective critical exponent of the transverse susceptibility found by matching techniques is scrutinized. It was first shown by Aharony and Fisher [l] that the short range Heisenberg fixed point (FP) of the renormalization group (RG) is unstable against perturbations from the long range dipole-dipole interaction leading to a new stable dipolar FP. In subsequent papers the crossover from a critical behavior dominated by the short range exchange interaction to the asymptotic dipolar critical behavior was investigated by parquet graph [2] and matching techniques [3]. The latter follow closely the concept of phenomenological crossover theory, which leads to several difficulties: (i) the use of two temperature variables makes the analysis quite complicated and (ii) one has to assume that the dipole-dipole interaction is sufficiently weak to guarantee that the RG trajectories traverse the region close to the unstable Heisenberg FP. In ferromagnets like EuO and EuS with relatively strong dipolar interaction this assumption may not be correct. Thus the dip in the effective susceptibility exponent yea (r) found by these earlier studies [2] may not be universal. Here we give a field theoretical description of the crossover solely in terms of the true reduced temperature r using a generalized minimal subtraction procedure introduced by Amit and Goldschmidt [4] for bicritical points. The Hamiltonian for a spin system with both exchange and dipolar interaction [I] is given by