| Crystalline membranes have rather unusual properties such as the absence of any finite elastic constants in the IR limit, anomalous fluctuations and a negative Poisson ratio. We use non-perturbative renormalization group techniques to calculate for the first time the full momentum dependence of thermal fluctuations of graphene, based on a non-local and non-linear ansatz for the elasticity of the membrane. We find a sharp crossover from the perturbative to the anomalous regime, in excellent agreement with Monte Carlo results for the the out-of-plane fluctuations of graphene, and give an accurate value for the crossover scale. Our work strongly supports the notion that graphene is well described as a standard crystalline membrane. We further show that ripples emerge naturally and are an inherent property of crystalline membranes. |
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