Crumpled-to-tubule transition in anisotropic polymerized membranes: beyond epsilon-expansion

TL;DR

This paper investigates the crumpled-to-tubule phase transition in anisotropic polymerized membranes using a nonperturbative renormalization group approach, overcoming limitations of previous perturbative methods.

Contribution

It introduces a nonperturbative RG framework to accurately analyze the transition, providing reliable critical quantities beyond epsilon-expansion.

Findings

Identifies the upper critical dimension as 2.5, close to D=2.

Shows perturbative approaches are inadequate for this transition.

Provides physically meaningful critical parameters for the phase transition.

Abstract

Anisotropic D-dimensional polymerized phantom membranes are investigated within a nonperturbative renormalization group (NPRG) framework. One focuses on the transition between a high-temperature, crumpled, phase and a low-temperature, tubular, phase where the membrane is flat along one direction and crumpled along the other ones. While the upper critical dimension - Duc=5/2 - is close to D=2 the weak-coupling perturbative approach is qualitatively and quantitatively wrong. We show that our approach is free of the problems encountered within the perturbative framework and provides physically meaningful critical quantities.