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.

arXiv comment10 pages, 10 figures. Final version to be published in PRE

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Cited by in corpus (10)

• Thermal crumpling of perforated two-dimensional sheets
• Thermalized buckling of isotropically compressed thin sheets
• The flat phase of polymerized membranes at two-loop order
• J-shaped stress-strain diagram of collagen fibers: Frame tension of triangulated surfaces with fixed boundaries
• Finsler geometry modeling and Monte Carlo study of 3D liquid crystal elastomer
• Finsler geometry modeling of phase separation in multi-component membranes
• Folding pathways to crumpling in thermalized elastic frames
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling
• Surface tension of membranes depending on the boundary shape