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 self-avoiding walk are examined using transfer matrix methods extended using DMRG 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 ($\nu$ and $\gamma$) is addressed, and the results found are at variance with previously conjectured exact values.