Critical behavior of magnets with dipolar interactions. II. Feynman-graph expansion for ferromagnets near four dimensions

The Feynman-graph-expansion approach of Wilson is used to study the critical behavior for 0<t=(TTc)-1GJad and H=0 of an isotropic ferromagnet in d=4-ε(ε>0) dimensions with exchange and dipolar interactions between d-component spins. [Here G=(g μB)22 measures the dipole-dipole interaction strength, J is the short-range exchange parameter, and a is the lattice spacing.] The susceptibility and the two-spin correlation functions are calculated to first order in ε, and agree with previous work, based on the renormalization-group approach. In addition the correlation function for transverse-spin fluctuations at Tc is investigated, yielding the critical exponent η20ε2867 [whereas for short-range exchange forces one has η3ε2122]. The limiting angular dependence of the four-spin correlation function is obtained.