Publication : t87/171

Abstract:
A field-theoretical model describing elastic membranes (2D membranes with inplane crystalline order and bending rigidity kappa) is presented and its renormalization studied. For large dimension D of bulk space, it is shown to have a nontrivial ultraviolet fixed point, that we associate to a second-order crumpling transition. This transition separates a crumpled phase for small kappa (characterized by an infinite Hausdorff dimension DH) from a rigid phase for large kappa (characterized by DH = 2 and spontaneous breaking of rotational invariance). The prediction for DH at the transition for large D is in reasonable agreement with numerical estimates at D = 3 and an exact result at D = 2.