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=(gμB)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 η≈20ε²867 [whereas for short-range exchange forces one has η≈3ε²12²]. The limiting angular dependence of the four-spin correlation function is obtained.