Critical behavior of magnets with dipolar interactions. V. Uniaxial magnets in D dimensions

The exact renormalization-group approach is used to study the critical behavior for T>Tc, H=0 of a uniaxial ferromagnetic (or ferroelectric) system in d dimensions, with exchange and dipolar interactions between the (single-component) spins. Normal Ising-like behavior is retained for t=TTc-1g^=(g μB)2Jad, where J is the exchange parameter, g μB is the magnetic moment per spin, and a is the lattice spacing. Crossover to a characteristic dipolar behavior occurs when tφg^, where φ=1+ε6 (to first order in ε=4-d). For tg^, the leading temperature singularity in the Fourier transform of the spin-spin correlation function Γ(q→) becomes ξ2×[1+(ξq)2-h0(ξqz)2+g0(qzq)2]-1, where h0 and g0 are of order g^ and ξ(t) varies as t-12 for d>3, as t-12|lnt|16 for d=3, and as t-ν with 12ν=1-(3-d)6+O((3-d)2) for d<3. The susceptibility displays the expected demagnetization effects, namely, (χ-1-g0D)ξ-2. The experimental situation is mentioned briefly.