Surface Critical Exponents in Terms of Bulk Exponents

The surface exponents associated with critical phenomena in semi-infinite systems are derived exactly in terms of bulk exponents. Results are γ1,1=ν-1, γ₁=ν+(γ-1)2, β₁=(3-α)2-ν, Δ₁=(1-α)2, η_∥=1ν, and η_⊥=1-(γ-1)2ν, where ν, γ, α, etc., are the standard bulk exponents. The bulk-surface crossover exponent is φₛ=1-ν. For ν>1 no surface phase can exist.