Crumpled-to-flat transition of quenched disordered membranes at two-loop order

TL;DR

This paper studies how quenched disorder influences the crumpling-to-flat transition in polymerized membranes, revealing potential new universality classes through a two-loop theoretical analysis near the critical dimension.

Contribution

It provides a two-loop computation showing disorder-induced second order transitions and the emergence of a new universality class in disordered membranes.

Findings

Disorder can induce second order transitions in membranes.

A new universality class may exist for disordered crumpling transitions.

Potential implications for membranes in three dimensions.

Abstract

We investigate the effects of quenched elastic disorder on the nature of the crumpling-to-flat transition of $D$-dimensional polymerized membranes using a two-loop computation near the upper critical dimension $D_c=4$. While the pure system undergoes fluctuation-induced first order transitions below $D_c$ and for an embedding dimension $d<d_{c,pure}\simeq 218.2$, one observes, in presence of disorder, the emergence of various regions of second order governed by a disordered stable fixed point for $d<d_{c1}\sim d_{c,pure}$. This opens the possibility of a new universality class associated with the crumpling-to-flat transition of disordered membranes in $d=3$