A Soluble Free-Fermion Model in d Dimensions

We consider a vertex model in d dimensions characterized by lines which run in a preferred direction. We show that this vertex model is soluble if the weights of vertices with intersecting lines are given by a free-fermion condition, and that a fugacity -1 is associated to each loop of lines. The solution is obtained by mapping the model into a dimer problem and by evaluating a Pfaffian. We also determine the critical point and the singular behavior of the free energy.