  We explore the phase diagram of an O(n) model on the honeycomb lattice with
vacancies, using finite-size scaling and transfer-matrix methods. We make use
of the loop representation of the O(n) model, so that $n$ is not restricted to
positive integers. For low activities of the vacancies, we observe critical
points of the known universality class. At high activities the transition
becomes first order. For n=0 the model includes an exactly known theta point,
used to describe a collapsing polymer in two dimensions. When we vary $n$ from
0 to 1, we observe a tricritical point which interpolates between the
universality classes of the theta point and the Ising tricritical point.
