Absence of an Ehrenfest Phase Transition in a Hard-Core Lattice Gas?

We report some numerical results for a lattice gas of hard-core molecules on the plane square lattice, occupancy of first, second, and fourth nearest neighbors to an occupied site being forbidden (1-2-4 model). Periodic lattices of even width up to 14 sites have been studied by the matrix method; the results indicate that any transition occurs at an activity $z_t=3.315\mathrm{}\pm 0.005$. However, there is evidence that the transition is not first order; indeed it is likely that no Ehrenfest phase transition (EPT) occurs in the model.