Spectrum of the Loop Transfer Matrix on Finite Lattices

We consider a model of random surfaces with extrinsic curvature term embedded into 3-D Euclidean lattice Z³. On a 3-D Euclidean lattice it has an equivalent representation in terms of the transfer matrix K(Q_i,Q_f), which describes the propagation of the loops Q. We study the spectrum of the transfer matrix K(Q_i,Q_f) on finite-dimensional lattices. The renormalisation group technique is used to investigate the phase structure of the model and its critical behaviour.