Critical Exponents for Long-Range Interactions

Critical exponents for a d-dimensional system with an isotropic n-component order parameter and long-range attractive interactions decaying as 1r^d+σ (σ>0) are derived, using the renormalization group approach, as power series in ε=2σ-d>0 (σ≠2, fixed) or Δσ=σ-1/2d>0 (d fixed) and, separately, to order 1/n for all d and σ≠2. For ε<0 the exponents have fixed ("classical") values; when ε=Δσ=0 fractional powers of ln(ΔTTc) appear; when σ>2 the exponents assume their short-range values.