Crumpling transition and flat phase of polymerized phantom membranes

TL;DR

This paper uses a nonperturbative renormalization group approach to study the phase transition and flat phase of polymerized membranes, providing insights into their critical behavior across dimensions.

Contribution

It introduces a comprehensive nonperturbative analysis of crumpling transition and flat phase in polymerized membranes across various dimensions, including the lower critical dimension.

Findings

Crumpling transition is second order in the studied approximation.

A weak first-order transition cannot be ruled out based on the results.

The approach determines the lower critical dimension for the phase transition.

Abstract

Polymerized phantom membranes are revisited using a nonperturbative renormalization group approach. This allows one to investigate both the crumpling transition and the low-temperature, flat, phase in any internal dimension D and embedding dimension d, and to determine the lower critical dimension. The crumpling phase transition for physical membranes is found to be of second order within our approximation. A weak first-order behavior, as observed in recent Monte Carlo simulations, is however not excluded.