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 ɛ=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 ɛ<0 the exponents have fixed ("classical") values; when ɛ=Δσ=0 fractional powers of ln(ΔTTc) appear; when σ>2 the exponents assume their short-range values.
- Publication:
-
Physical Review Letters
- Pub Date:
- October 1972
- DOI:
- 10.1103/PhysRevLett.29.917
- Bibcode:
- 1972PhRvL..29..917F