Surface critical behaviour of the vertex-interacting self-avoiding walk on the square lattice.

The phase diagram and surface critical behaviour of the vertex-interacting selfavoiding walk are examined using transfer matrix methods extended using the density matrix renormalization group method and coupled with finite-size scaling. Particular attention is paid to the critical exponents at the ordinary and special points along the collapse transition line. The question of the bulk exponents (? and ? ) is addressed, and the results found are at variance with previously conjectured exact values. [ABSTRACT FROM AUTHOR]