Transfer Matrix Algorithm for Computing the Geometric Quantities of a Square Lattice Polymer

Abstract

I develop a transfer matrix algorithm for computing the geometric quantities of a square lattice polymer with nearest-neighbor interactions. The radius of gyration, the end-to-end distance, and the monomer-to-end distance were computed as functions of the temperature. The computation time scales as less than or similar to 1.8(N) with a chain length N, in contrast to the explicit enumeration where the scaling is similar to 2.7(N). Various techniques for reducing memory requirements are implemented.