Statistical Mechanics of Self-Avoiding Manifolds (Part II)
arXiv:cond-mat/0408407 · doi:10.1142/9789812565518_0009
Abstract
We consider a model of a D-dimensional tethered manifold interacting by excluded volume in R^d with a single point. Use of intrinsic distance geometry provides a rigorous definition of the analytic continuation of the perturbative expansion for arbitrary D, 0 < D < 2. Its one-loop renormalizability is first established by direct resummation. A renormalization operation R is then described, which ensures renormalizability to all orders. The similar question of the renormalizability of the self-avoiding manifold (SAM) Edwards model is then considered, first at one-loop, then to all orders. We describe a short-distance multi-local operator product expansion, which extends methods of local field theories to a large class of models with non-local singular interactions. It vindicates the direct renormalization method used earlier in part I of these lectures, as well as the corresponding scaling laws.
32 pages, 9 figures, Second Part and extensive update of Lecture Notes originally given in ``Statistical Mechanics of Membranes and Surfaces'', Fifth Jerusalem Winter School for Theoretical Physics (1987), D. R. Nelson, T. Piran,and S. Weinberg eds