RENORMALIZATION-GROUP RESULTS FOR LATTICE SURFACE MODELS

We study the phase diagram of statistical systems of closed and open i nterfaces built on a cubic lattice. Interacting closed interfaces can be written as Ising models, while open surfaces can be written as Z(2) gauge systems. When the open surfaces reduce to closed interfaces wit h few defects, the gauge model can be also written as an Ising spin mo del. We apply the lower bound renormalization group (LBRG) transformat ion introduced by Kadanoff (1975 Phys. Rev. Lett. 34 1005) to study th e Ising models describing closed and open surfaces with few defects. I n particular, we have studied the Ising-like transition of self-avoidi ng surfaces between the random isotropic phase and the phase with brok en global symmetry at varying values of the mean curvature. Our result s are compared with previous numerical work. The limits of the LBRG tr ansformation in describing regions of the phase diagram where non-ferr omagnetic ground states are relevant are also discussed.