Self-Avoiding Random Manifolds

TL;DR

This paper reviews the physics of flexible random manifolds, focusing on self-avoidance effects and their renormalization group treatment, with applications to polymerized membranes and crumpling transitions.

Contribution

It provides a comprehensive overview of self-avoiding random manifolds, integrating theories of membrane physics and non-local field approaches, highlighting recent advances.

Findings

Self-avoidance significantly influences membrane configurations.

Renormalization group methods effectively analyze self-avoidance effects.

Connections to polymer physics and crumpling transitions are elucidated.

Abstract

These lectures deal with: (1) a brief review of the theory of flexible random manifolds (with fixed intrinsic metric), connected to the physics of polymerized membranes, and of the effect of extrinsic curvature (crumpling transitions); (2) a discussion of the effect of self-avoidance and its renormalization group treatment in term of a non-local field theory (this last part is not much different from cond-mat/9509096).