Conformation of Linear Polymers in Three Dimensions

By significantly extending the existing exact enumeration results, and by combining several independent analysis methods, the authors obtain accurate estimates of the leading "scaling" exponent and the amplitudes for the $d=3\mathrm{}$ linear-polymer radius-of-gyration problem. Specifically, they find that the mean square end-to-end distance of an $N$-step self-avoiding walk on an fcc lattice is given by the expression ${\rho }_N\sim A{N}^{2\nu }[1+\frac{B}{N^{\Delta }}+\frac{C}{N}]$ with $\nu \cong 0.5875$, $\Delta \cong 0.470$, $A\cong 1.05$, $B\cong \frac{-0.3\mathrm{}}{A}$, and $C\cong 0.25$.