Thermal Buckling Transition of Crystalline Membranes in a Field

Two dimensional crystalline membranes in isotropic embedding space exhibit a flat phase with anomalous elasticity, relevant e.g., for graphene. Here we study their thermal fluctuations the absence of exact rotational invariance space. An example is provided by membrane an orientational field, tuned to critical buckling point application in-plane stresses. Through detailed analysis, show that transition new universality class. The self-consistent screening method predicts second order transition, modified elasticity exponents at criticality, while RG suggests weakly first transition.