Thermalized buckling of clamped plates

Atomically thin free-standing 2D materials such as graphene offer new opportunities to revisit classic mechanical instabilities such as the Euler buckling transition. In such fragile materials, thermal fluctuations dominate and dramatically renormalize the elastic moduli of the membrane. By focusing on geometrically confined thin sheets, we are able to investigate the interplay between boundary conditions and thermal fluctuations in controlling buckling. Remarkably, clamped boundary conditions induce a novel long-ranged nonlinear interaction between the local tilt at distant points, which along with a spontaneously generated thermal tension leads to a renormalization group description of thermalized buckling as an unusual phase transition with a size dependent critical point.