title: Universal behavior of crystalline membranes: Crumpling transition and Poisson ratio of the flat phase.
abstract: We revisit the universal behavior of crystalline membranes at and below the crumpling transition, which pertains to the mechanical properties of important soft and hard matter materials, such as the cytoskeleton of red blood cells or graphene. Specifically, we perform large-scale Monte Carlo simulations of a triangulated two-dimensional phantom network which is freely fluctuating in three-dimensional space. We obtain a continuous crumpling transition characterized by critical exponents which we estimate accurately through the use of finite-size techniques. By controlling the scaling corrections, we additionally compute with high accuracy the asymptotic value of the Poisson ratio in the flat phase, thus characterizing the auxetic properties of this class of systems. We obtain agreement with the value which is universally expected for polymerized membranes with a fixed connectivity.
authors.affiliation: Departamento de Matemáticas and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Carlos III, 28911 Leganés, Spain.
authors.forename: R
authors.initials: R
authors.lastname: Cuerno
authors.affiliation: Departamento de Electrónica and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071 Badajoz, Spain.
authors.forename: R
authors.initials: R
authors.lastname: Gallardo Caballero
authors.affiliation: Departamento de Electrónica and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071 Badajoz, Spain.|Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain.
authors.forename: A
authors.initials: A
authors.lastname: Gordillo-Guerrero
authors.affiliation: Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.
authors.forename: P
authors.initials: P
authors.lastname: Monroy
authors.affiliation: Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain.|Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071 Badajoz, Spain.
authors.forename: J J
authors.initials: JJ
authors.lastname: Ruiz-Lorenzo
mesh_terms: D001696:Biomechanical Phenomena; D055595:Mechanical Phenomena; D008567:Membranes, Artificial; D008968:Molecular Conformation; D009010:Monte Carlo Method; D016012:Poisson Distribution; D011108:Polymers / Q000737:chemistry
chemical_list: D008567:Membranes, Artificial; D011108:Polymers