Calculation of subcritical exponents for corrections to scaling

Abstract

The "subcritical" exponent ${\Delta }_{2s}$ for corrections to asymptotic scaling in the renormalization-group theory of critical phenomena, has been calculated for the continuous-spin versions of the classical, $d=3\mathrm{}$ Ising, $X-Y$, and Heisenberg models by numerical integrations of Wilson's approximate recursion formula. The results are ${\Delta }_{2s}\left(\mathrm{Ising}\right)=-0.640\mathrm{}$, ${\Delta }_{2s}(X-Y)=-0.644\mathrm{}$, and ${\Delta }_{2s}\left(\mathrm{Heisenberg}\right)=-0.647\mathrm{}$. Comparison is made with results from perturbation expansions in $\epsilon =4-d$ ($d$ being the dimensionality), high-temperature series expansions, and experimental measurements.