The paper by Fasolino, Los, and Katsnelson explores the intrinsic ripples in graphene, a two-dimensional (2D) crystal. The authors use atomistic Monte Carlo simulations based on an accurate many-body interatomic potential for carbon to investigate the stability and structure of graphene. They find that ripples spontaneously appear due to thermal fluctuations, with a size distribution peaked around 70 Å, which is consistent with experimental observations but not with current theories of flexible membranes. The results deviate from harmonic behavior, showing a marked maximum in fluctuations at a wavelength of about 70 Å. This deviation is attributed to the multiplicity of chemical bonding in carbon, leading to partial changes from conjugated to single/double bonds and deviations from planarity. The study also reveals a stiffening of the bending rigidity with increasing temperature. The findings have implications for understanding the electronic transport properties of graphene, as fluctuations in the normals can modulate hopping integrals and affect the electronic structure.The paper by Fasolino, Los, and Katsnelson explores the intrinsic ripples in graphene, a two-dimensional (2D) crystal. The authors use atomistic Monte Carlo simulations based on an accurate many-body interatomic potential for carbon to investigate the stability and structure of graphene. They find that ripples spontaneously appear due to thermal fluctuations, with a size distribution peaked around 70 Å, which is consistent with experimental observations but not with current theories of flexible membranes. The results deviate from harmonic behavior, showing a marked maximum in fluctuations at a wavelength of about 70 Å. This deviation is attributed to the multiplicity of chemical bonding in carbon, leading to partial changes from conjugated to single/double bonds and deviations from planarity. The study also reveals a stiffening of the bending rigidity with increasing temperature. The findings have implications for understanding the electronic transport properties of graphene, as fluctuations in the normals can modulate hopping integrals and affect the electronic structure.