Renormalization-group calculation of critical exponents for three-dimensional Ising-like systems

Abstract

A modification of the Wilson-Kogut smooth-cutoff formulation of the renormalization group is developed. The resulting hierarchy of equations is truncated at four levels, with the renormalization-group parameters being approximated by the leading terms of a mometum-space Taylor series. The equations are then solved for $d=3\mathrm{}$, $N=1\mathrm{}$ systems. A line of fixed points with associated $\eta \cong 0.045$ is obtained. The largest two eigenvalues of the near-fixed-point hierarchy are $y_1\cong 1.6$ and $y_2\cong -1.6\mathrm{}$.