On the reformulation of the d = 3 Ising model in terms of random surfaces

Abstract

We derive equations of motion or order-disorder variables in the d = 2 and d = 3 Ising models, working directly on the lattice. The integration of these equations leads to a reformulation of the d = 2 Ising model in terms of random paths (this is obvious) and to a reformulation of the d = 3 Ising model in terms of random surfaces (this is new).