Transfer matrix algorithm for computing the exact partition function of a square lattice polymer

I develop a transfer matrix algorithm for computing the exact partition function of a square lattice polymer with nearest-neighbour interactions by extending a previous algorithm for computing the total number of self-avoiding walks. The computation time scales as ∼1.6N with the chain length N, in contrast to the explicit enumeration where the scaling is ∼2.7N. The exact partition function can be obtained faster with the transfer matrix method than with the explicit enumeration for N>25. The new results for up to N=42 are presented.