RENORMALIZATION AND HYPERSCALING FOR SELF-AVOIDING MANIFOLD MODELS

The renormalizability of the self-avoiding manifold Edwards model is established. We use a new short distance multilocal operator product expansion, which extends methods of local field theories to a large class of models with nonlocal singular interactions. This validates the direct renormalization method introduced before, as well as scaling laws. A new general hyperscaling relation is derived. Manifolds at the THETA point and long-range Coulomb interactions are briefly discussed.