Tethering, Crumpling, and Melting Transitions in Hexatic Membranes

We consider membranes with bending rigidity and internal hexatic orientational order. For crumpled membranes, in the absence of disclinations, the internal metric undergoes a transition between tethered and liquidlike behaviors. However, this “tethering” transition is destroyed upon inclusion of disclinations, coupled to suitable conical deformations of the membrane. Critical properties at “crumpling” and “melting” transitions of high-rigidity membranes are examined. We suggest that, upon inclusion of self-avoiding effects, the behaviors of hexatic and tethered surfaces are very similar.