First and second order transitions in dilute O(n) models

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 restrict ed to positive integers. For low activities of the vacancies, we observe cr itical points of the known universality class. At high activities the trans ition becomes first order. For n = 0 the model includes an exactly known th eta 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 betw een the universality classes of the theta point and the Ising tricritical p oint.