Renormalization-Group Calculation of Critical Exponents in Three Dimensions

A scaling-field representation of Wilson's exact renormalization-group equation is derived and used for the approximate calculation of critical exponents for the continuous-spin Ising model in three dimensions. The truncation of the hierarchy of scaling-field equations that retains only the four most relevant scaling fields yields the critical exponents $\nu \approx 0.60$, $\eta \approx 0.06$, and ${\Delta }_1\approx -0.47\mathrm{}$ (where ${\Delta }_1$ denotes Wortis's correction-to-scaling exponent).