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 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 (ν and γ) is addressed, and the results found are at variance with previously conjectured exact values.