A family of two-dimensional spin models with $n$-spin interactions in one direction and two-spin interactions in the other is studied by Monte Carlo simulations. Our results show that for the case where the variables are of the Ising ($q$-state Potts, $q>\mathrm{}2\mathrm{}$) type the transition is of first order for $n>\mathrm{}{n}_c=3\mathrm{} (n>\mathrm{}{n}_c=2)$ in agreement with previous conjecture.

• Received 17 June 1986

DOI:https://doi.org/10.1103/PhysRevB.34.4885