Renormalization and Hyperscaling for Self-Avoiding Manifold Models

TL;DR

This paper establishes the renormalizability of the self-avoiding manifold model using a novel multilocal operator product expansion, deriving a new hyperscaling relation and discussing special cases like the Theta-point.

Contribution

It introduces a new multilocal operator product expansion method to prove renormalizability and derive hyperscaling laws for self-avoiding manifold models.

Findings

Renormalizability of the SAM Edwards model is proven.

A new hyperscaling relation for the configuration exponent gamma is derived.

The approach extends local field theory methods to non-local interactions.

Abstract

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