Critical line of an n-component cubic model.

We consider a special case of the -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 . Furthermore we determine several universal quantities, including three critical exponents. For , these results agree well with the theoretical predictions for the critical branch. This model is also a special case of the model of Domany and Riedel. It appears that the self-dual plane of the latter model contains the exactly known critical points of the and 2 cubic models. For this reason we have checked whether this is also the case for . However, this possibility is excluded by our numerical results.