Critical behavior in graphene: spinodal instability at room temperature

At a critical spinodal in-plane stress $\tau_{C}$ a planar crystalline graphene layer becomes mechanically unstable. We present a model of the critical behavior of the membrane area near $\tau_{C}$ and show that it is in complete agreement with path-integral simulations and with recent experiments based on interferometric profilometry and Raman spectroscopy. Close to the critical stress, $\tau_{C}$, the in-plane strain behaves as $\left(\tau_{C}-\tau\right)^{1/2}$ for $\tau<\tau_{C}$.