Critical Behavior of Magnets with Dipolar Interactions. V. Uniaxial Magnets indDimensions

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-1^g=(gμB)²Jaᵈ, where J is the exchange parameter, gμB is the magnetic moment per spin, and a is the lattice spacing. Crossover to a characteristic dipolar behavior occurs when t^φ≈^g, where φ=1+ε6 (to first order in ε=4-d). For t^g, 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^-1/2 for $d>3$, as t^-1/2|lnt|1/6 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.