The Crumpling Transition Revisited

TL;DR

This paper revisits the crumpling transition in surfaces, examining whether it is a second or higher order transition, and discusses lattice artifacts and model distinctions affecting the transition order.

Contribution

It clarifies the nature of the crumpling transition, analyzing lattice models and addressing discrepancies in transition order reports.

Findings

Some lattice models show artifacts affecting transition order

Models indistinguishable from second order can exhibit third order transitions

The transition order may depend on model specifics and lattice effects

Abstract

The ``crumpling" transition, between rigid and crumpled surfaces, has been object of much discussion over the past years. The common lore is that such transition should be of second order. However, some lattice versions of the rigidity term on fixed connectivity surfaces seem to suggest that the transition is of higher order instead. While some models exhibit what appear to be lattice artifacts, others are really indistiguishable from models where second order transitions have been reported and yet appear to have third order transitions.