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 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. 
Wenan Guo, Henk W.J. Bloete (Delft University of Technology) and   Bernard Nienhuis (Universiteit van Amsterdam)