  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 in the absence of exact rotational invariance
in the embedding space. An example is provided by a membrane in an
orientational field, tuned to a critical buckling point by application of
in-plane stresses. Through a detailed analysis, we show that the transition is
in a new universality class. The self-consistent screening method predicts a
second order transition, with modified anomalous elasticity exponents at
criticality, while the RG suggests a weakly first order transition.
