Crumpling transition and flat phase of polymerized phantom membranes

Abstract

Polymerized phantom membranes are revisited using a nonperturbative renormalization group approach. This allows one to investigate both the crumpling transition and the low-temperature, flat, phase in any internal dimension D and embedding dimension d, and to determine the lower critical dimension. The crumpling phase transition for physical membranes is found to be of second order within our approximation. A weak first-order behavior, as observed in recent Monte Carlo simulations, is however not excluded.

4 pages, 1 figure, version published in PRE

References in corpus (11)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Exact Renormalization Group Equations. An Introductory Review
• Self-Consistent Theory of Polymerized Membranes
• Critical exponents from optimised renormalisation group flows
• Nonperturbative renormalization group approach to frustrated magnets
• The Statistical Mechanics of Membranes
• The Flat Phase of Crystalline Membranes
• First-order transition of tethered membranes in 3d space
• First-order phase transition of fixed connectivity surfaces
• M.C.R.G. Study of Fixed-connectivity Surfaces

Cited by in corpus (78)

• The nonperturbative functional renormalization group and its applications
• Novel effects of strains in graphene and other two dimensional materials
• Scaling Properties of Flexible Membranes from Atomistic Simulations: Application to Graphene
• Scaling behavior and strain dependence of in-plane elastic properties of graphene
• Suppression of anharmonicities in crystalline membranes by external strain
• Graphene as a Prototype Crystalline Membrane
• Mermin-Wagner theorem, flexural modes, and degraded carrier mobility in 2D crystals with broken horizontal mirror (${\sigma }_{\mathrm{h}}$) symmetry
• Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Response of thermalized ribbons to pulling and bending
• The Structure of Physical Crystalline Membranes within the Self-Consistent Screening Approximation
• Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene
• Anomalous elasticity, fluctuations and disorder in elastic membranes
• Thermal fluctuations of free standing graphene
• Conductivity of suspended graphene at the Dirac point
• Non-Hookean statistical mechanics of clamped graphene ribbons
• Quantum elasticity of graphene: Thermal expansion coefficient and specific heat
• Stress-controlled Poisson ratio of a crystalline membrane: Application to graphene
• Rippling and crumpling in disordered free-standing graphene
• Thermodynamics of quantum crystalline membranes
• First order phase transitions in polymerized phantom membranes
• Statistical mechanics of thin spherical shells
• Differential Poisson's ratio of a crystalline two-dimensional membrane
• High Precision Fourier Monte Carlo Simulation of Crystalline Membranes
• Nonlocal effective average action approach to crystalline phantom membranes
• Flexuron, a self-trapped state of electron in crystalline membranes
• Crumpled-to-tubule transition in anisotropic polymerized membranes: beyond epsilon-expansion
• Buckling of thermalized elastic sheets
• Thermal crumpling of perforated two-dimensional sheets
• Monte Carlo studies of a Finsler geometric surface model
• Thermalized buckling of isotropically compressed thin sheets
• A glassy phase in quenched disordered graphene and crystalline membranes
• Scaling behavior of crystalline membranes: an $\epsilon$-expansion approach
• The flat phase of polymerized membranes at two-loop order
• The flat phase of quantum polymerized membranes
• Thermal buckling and symmetry breaking in thin ribbons under compression
• Fluid Membranes and 2d Quantum Gravity
• Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets
• Thermal stiffening of clamped elastic ribbons
• Thermal buckling transition of crystalline membranes in a field
• Scale without conformal invariance in membrane theory
• Absolute Poisson's ratio and the bending rigidity exponent of a crystalline two-dimensional membrane
• Finsler geometry modeling and Monte Carlo study of 3D liquid crystal elastomer
• Three-loop order approach to flat polymerized membranes
• Universal behavior of crystalline membranes: crumpling transition and Poisson ratio of the flat phase
• Bending rigidity, sound propagation and ripples in flat graphene
• Fourier Monte Carlo Renormalization Group Approach to Crystalline Membranes
• Disorder-induced rippled phases and multicriticality in free-standing graphene
• Spontaneous tilt of single-clamped thermal elastic sheets
• Thermal ripples in bilayer graphene
• Dynamical Eigenmodes of a Polymerized Membrane
• Crumpling transition of the discrete planar folding in the negative-bending-rigidity regime
• Interplay between nanometer-scale strain variations and externally applied strain in graphene
• Effective average action based approach to correlation functions at finite momenta
• Spontaneous symmetry breaking and the flat phase of crystalline membranes
• Distribution of ripples in graphene membrane
• Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule
• Wrinkling transition in quenched disordered membranes at two loops
• Monte Carlo studies of triangulated spherical surfaces in the two-dimensional space
• Finsler geometry modeling of phase separation in multi-component membranes
• Four-loop critical properties of polymerized membranes
• Universal behaviors in the wrinkling transition of disordered membranes
• Renormalization Group Flow of Hexatic Membranes
• Flat phase of quenched disordered membranes at three-loop order
• Stiffening Thermal Membranes by Cutting
• Branched-polymer to inflated transition of self-avoiding fluid surfaces
• Thermal fluctuations in crystalline membranes with long-range dipole interactions
• Flat polymerized membranes at three-loop order
• Parallel tempering Monte Carlo simulations of spherical fixed-connectivity model for polymerized membranes
• 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
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order
• Geometric control of tilt transition dynamics in single-clamped thermalized elastic sheets
• First-order phase transition of triangulated surfaces on a spherical core
• Shape transformations of a model of self-avoiding triangulated surfaces of sphere topology
• Perturbative renormalization and thermodynamics of quantum crystalline membranes
• Renormalization group approach to the elastic properties of graphene bilayers
• In-plane deformation of a triangulated surface model with metric degrees of freedom