The flat phase of polymerized membranes at two-loop order

Abstract

We investigate two complementary field-theoretical models describing the flat phase of polymerized - phantom - membranes by means of a two-loop, weak-coupling, perturbative approach performed near the upper critical dimension $D_{uc}=4$, extending the one-loop computation of Aronovitz and Lubensky [Phys. Rev. Lett. 60, 2634 (1988)]. We derive the renormalization group equations within the modified minimal substraction scheme, then analyze the corrections coming from two-loop with a particular attention paid to the anomalous dimension and the asymptotic infrared properties of the renormalization group flow. We finally compare our results to those provided by nonperturbative techniques used to investigate these two models.

arXiv comment9 pages, 1 figure, published version

References in corpus (47)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Aspects of the Functional Renormalisation Group
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• Exact Renormalization Group Equations. An Introductory Review
• Self-Consistent Theory of Polymerized Membranes
• Fundamentals of the Exact Renormalization Group
• Nonperturbative renormalization group approach to frustrated magnets
• The Statistical Mechanics of Membranes
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• Scaling Properties of Flexible Membranes from Atomistic Simulations: Application to Graphene
• Crumpling transition and flat phase of polymerized phantom membranes
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Scaling behavior and strain dependence of in-plane elastic properties of graphene
• Suppression of anharmonicities in crystalline membranes by external strain
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• The Flat Phase of Crystalline Membranes
• 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
• Two loop results from one loop computations and non perturbative solutions of exact evolution equations
• Thermal fluctuations of free standing graphene
• First-order transition of tethered membranes in 3d space
• Universality Classes of Self-Avoiding Fixed-Connectivity Membranes
• Multi-loop techniques for massless Feynman diagram calculations
• Convergence of derivative expansions of the renormalization group
• Rippling and crumpling in disordered free-standing graphene
• First-order phase transition in the tethered surface model on a sphere
• Statistical mechanics of thin spherical shells
• First order phase transitions in polymerized phantom membranes
• High Precision Fourier Monte Carlo Simulation of Crystalline Membranes
• Nonlocal effective average action approach to crystalline phantom membranes
• First-order phase transition of fixed connectivity surfaces
• Crumpled-to-tubule transition in anisotropic polymerized membranes: beyond epsilon-expansion
• Quantum and classical ripples in graphene
• Scaling behavior of crystalline membranes: an $\epsilon$-expansion approach
• A glassy phase in quenched disordered graphene and crystalline membranes
• The flat phase of quantum polymerized membranes
• Absolute Poisson's ratio and the bending rigidity exponent of a crystalline two-dimensional membrane
• Universal behavior of crystalline membranes: crumpling transition and Poisson ratio of the flat phase
• Fourier Monte Carlo Renormalization Group Approach to Crystalline Membranes
• Spontaneous symmetry breaking and the flat phase of crystalline membranes
• Monte Carlo simulations of Landau-Ginzburg model for membranes
• Universal behaviors in the wrinkling transition of disordered membranes
• Parallel tempering Monte Carlo simulations of spherical fixed-connectivity model for polymerized membranes

Cited by in corpus (16)

• Buckling of thermalized elastic sheets
• Scale and Conformal Invariance in Higher Derivative Shift Symmetric Theories
• Thermal buckling transition of crystalline membranes in a field
• Scale without conformal invariance in membrane theory
• Three-loop order approach to flat polymerized membranes
• Thermal ripples in bilayer graphene
• Wrinkling transition in quenched disordered membranes at two loops
• Emergent continuous symmetry in anisotropic flexible two-dimensional materials
• Flat phase of quenched disordered membranes at three-loop order
• Disorder-driven transition to tubular phase in anisotropic two-dimensional materials
• Flat polymerized membranes at three-loop order
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• Geometric control of tilt transition dynamics in single-clamped thermalized elastic sheets
• Geometrically-induced localization of flexural waves on thin warped physical membranes
• Perturbative renormalization and thermodynamics of quantum crystalline membranes
• Renormalization group approach to the elastic properties of graphene bilayers