Loop transfer matrix and gonihedric loop diffusion

We study a class of statistical systems which simulate 3D gonihedric system on euclidean lattice. We have found the exact partition function of the 3D-model and the corresponding critical indices analysing the transfer matrix $K(P_i,P_f)$ which describes the propagation of loops on a lattice. The connection between 3D gonihedric system and 2D-Ising model is clearly seen.