Diffusion of Loops

We study a lattice model that is closely related to the Ising model and can be regarded as describing diffusion of loops in two dimensions. The time development is given by a transfer matrix for a random surface model on a three-dimensional lattice. The transfer matrix is indexed by loops and is invariant under a group of motions in the loop space. The eigenvalues of the transfer matrix are calculated in terms of the partition function and the correlation functions of the Ising model.