Critical Exponents for Long-Range Interactions

Abstract

Critical exponents for a d-dimensional system with an isotropic n-component order parameter and long-range attractive interactions decaying as 1rd+σ (σ>0) are derived, using the renormalization group approach, as power series in ε=2σ−d>0 (σ≠2, fixed) or Δσ=σ−12d>0 (d fixed) and, separately, to order 1n for all d and σ≠2. For ε2 the exponents assume their short-range values.