Critical line of an n-component cubic model

We consider a special case of the n-component cubic model on the square lattice, for which an expansion exists in Ising-type graphs. We construct a transfer matrix and perform a finite-size-scaling analysis to determine the critical points for several values of n. Furthermore we determine several universal quantities, including three critical exponents. For n < 2, these results agree well with the theoretical predictions for the critical O(n) branch. This model is also a special case of the (N-alpha,N-beta) model of Domany and Riedel. It appears that the self-dual plane of the latter model contains the exactly known critical points of the n=1 and 2 cubic models. For this reason we have checked whether this is also the case for 1 < n < 2. However, this possibility is excluded by our numerical results.