  We numerically investigate the influence of self-attraction on the critical
behaviour of a polymer in two dimensions, by means of an analysis of
finite-size results of transfer-matrix calculations. The transfer matrix is
constructed on the basis of the O($n$) loop model in the limit $n \to 0$. It
yields finite-size results for the magnetic correlation length of systems with
a cylindrical geometry. A comparison with the predictions of finite-size
scaling enables us to obtain information about the phase diagram as a function
of the chemical potential of the loop segments and the strength of the
attractive potential. Results for the magnetic scaling dimension can be
interpreted in terms of known universality classes. In particular, when the
attractive potential is increased, we observe the crossover between polymer
critical behaviour of the self-avoiding walk type to behaviour described
earlier for the theta point.

Statistical Mechanics