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The phase diagram for a two-dimensional self-avoiding walk model on thesquare lattice incorporating attractive short-ranged interactions betweenparallel sections of walk is derived using numerical transfer matrixtechniques. The model displays a collapse transition. In contrast to thestandard $\theta$-point model, the transition is first order. The phase diagramin the full fugacity-temperature plane displays an additional transition line,when compared to the $\theta$-point model, as well as a critical transition atfinite temperature in the hamiltonian walk limit.Comment: 22 pages, 13 figures. To appear in Journal of Physics

Two-dimensional self-avoiding walk with hydrogen-like bonding: phase diagram and critical behaviour