2009/03/23 by J. H. Los, J. Los, M. I. Katsnelson +5 · 171 citations
Engineering · Materials Science · Physics and Astronomy · #Condensed matter physics #Exponent #Graphene #Graphene research and applications #Molecular dynamics #Monte Carlo method #Nanopore and Nanochannel Transport Studies #Physics #Quantum mechanics #Scaling #Scaling law #Statistical physics #Statistics #Surface and Thin Film Phenomena #Wave function #cond-mat.mtrl-sci #cond-mat.soft
paper · pdf · doi:10.1103/physrevb.80.121405
published in Physical Review B 80(12) (American Physical Society)
arxiv created 2009/03/23 · openalex publication_date 2009/09/23 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Structure and thermodynamics of crystalline membranes are characterized by the long-wavelength behavior of the normal-normal correlation function G(q). We calculate G(q) by Monte Carlo and molecular dynamics simulations for a quasiharmonic model potential and for a realistic potential for graphene. To access the long-wavelength limit for finite-size systems (up to 40 000 atoms) we introduce a Monte Carlo sampling based on collective atomic moves (wave moves). We find a power-law behavior G(q)\ensuremath∝q^\ensuremath-2+\ensuremathη with the same exponent \ensuremathη\ensuremath≈0.85 for both potentials. This finding supports, from the microscopic side, the adequacy of the scaling theory of membranes in the continuum medium approach, even for an extremely rigid material such as graphene.