Dynamics of Selfavoiding Tethered Membranes I Model A Dynamics (Rouse Model)

TL;DR

This paper investigates the dynamic scaling behavior of self-avoiding polymerized membranes using model A dynamics, establishing a renormalizable theory and deriving a universal scaling exponent applicable to membranes and polymers.

Contribution

It provides a rigorous proof of the dynamical scaling exponent z=2+D/nu for self-avoiding membranes and polymers, confirming a previously suggested relation.

Findings

The theory is renormalizable to all orders.

The dynamical scaling exponent z=2+D/nu is derived.

The results apply to both membranes (D=2) and polymers (D=1).

Abstract

The dynamical scaling properties of selfavoiding polymerized membranes with internal dimension D are studied using model A dynamics. It is shown that the theory is renormalizable to all orders in perturbation theory and that the dynamical scaling exponent z is given by z=2+D/nu. This result applies especially to membranes (D=2) but also to polymers (D=1), for which this scaling relation had been suggested but not proven.