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

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.

4 pages, 3 figures

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• Exact evolution equation for the effective potential
• Crumpling transition and flat phase of polymerized phantom membranes
• Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene
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