Self-avoiding Tethered Membranes at the Tricritical Point

TL;DR

This paper investigates the critical behavior of self-avoiding tethered membranes at the tricritical point using advanced renormalization group techniques, revealing the relevance of long-range interactions in two dimensions.

Contribution

It develops new analytical and numerical tools for 1-loop calculations and introduces a double epsilon-expansion to study interaction cross-over in self-avoiding membranes.

Findings

Long-range attractive interactions are relevant at the theta-point for 2D membranes.

New methods enable higher order calculations for self-avoiding membranes.

The cross-over between 3-body and 2-body interactions is characterized.

Abstract

The scaling properties of self-avoiding tethered membranes at the tricritical point (theta-point) are studied by perturbative renormalization group methods. To treat the 3-body repulsive interaction (known to be relevant for polymers), new analytical and numerical tools are developped and applied to 1-loop calculations. These technics are a prerequisite to higher order calculations for self-avoiding membranes. The cross-over between the 3-body interaction and the modified 2-body interaction, attractive at long range, is studied through a new double epsilon-expansion. It is shown that the latter interaction is relevant for 2-dimensional membranes at the theta-point.