The crumpling transition revisited

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 transtion should be of second order. However, some lattice versions of the rigidity term on fixed connectivity surfaces seem to suggest that the trnsition is of higher order instead. While some models exhibit what appear to be lattice artifacts, others are really indistinguishable from models where second order transitions have been reported and yet appear to have third order transitions.