Reassessment of critical exponents and corrections to scaling for self-avoiding walks

The exact enumeration series of the radius of gyration $S_N$ for self-avoiding walks are analyzed for various lattices in three and two dimensions (3D and 2D) in addition to those of the end-to-end distance $R_N$ and the number of walks $C_N$ using a method newly developed. The estimates of ν for $R_N$ and γ for $C_N$ are in good agreement with the renormalization-group calculations in 3D and Nienhuis’s analytical results in 2D; the estimates of ν for $S_N$ in both 3D and 2D are somewhat greater than those for $R_N$. The average estimates of the correction-to-scaling exponent ${\Delta }_1$ are ${\Delta }_1$=0.48 (3D) and 0.65 (2D) for $R_N$, and ${\Delta }_1$=1.19 (3D) and 1.06 (2D) for $S_N$, while ${\Delta }_1$=0.99 (3D) and 0.97 (2D) for $C_N$.