Ising Model with Four-Spin Interactions

It is shown that Baxter's recent results on a lattice-statistical model lead to the solution of an Ising model with two- and four-spin interactions. Critical properties of this Ising model in various regions of the parameter space are given. It is argued that four-spin or crossing interactions in a two-dimensional Ising model would in general lead to a critical exponent ${\alpha }^{\prime }\ne 0$.