Critical exponents for cubic and impure uniaxial crystals: most accurate (?) theoretical values

Abstract

RG functions are calculated up to 4-loop order in 3 and 2 dimensions to evaluate, within Chisholm-Borel resummation technique, critical exponents for cubic and impure uniaxial crystals and the order parameter critical dimensionality n_c . For 3D impure Ising crystals γ = 1.326, v = 0.670, α = -0.011, β = 0.342, η = 0.034, while critical exponents of 3D cubic crystals practically coincide with those of the Heisenberg model; n_c = 2.9. For 2D systems the fermion representation enables us to find that their critical behavior is identical to that of pure Ising model, apart some logarithmic factors.