Direct Enumeration Study of Self-Avoiding Walks on the Tetrahedral Lattice

Abstract

By application of a general procedure devised by Martin, we generated, up to $\text{N\hspace{0.17em}=\hspace{0.17em}14}$ , the number of self‐avoiding open chains, and determined their mean‐square end‐to‐end distance, their radius of gyration, the number of returns to the origin, and its corresponding mean‐square end‐to‐end distances. The self‐avoiding chain results were in excellent agreement with Monte Carlo calculations, and the mean‐square radius of gyration of ring systems agreed with our previous Monte Carlo estimates. The number of returns to the origin was used to calculate the order of a phase transition for a tetrahedral model of the helix‐to‐random‐coil system. The higher‐order transition found is the same as that previously obtained by Fisher for other three‐dimensional model systems.