First order phase transitions in polymerized phantom membranes

Abstract

The crumpled-to-flat phase transition that occurs in D-dimensional polymerized phantom membranes embedded in a d-dimensional space is investigated nonperturbatively using a field expansion up to order eight in powers of the order parameter. We get the critical dimension dcr(D) that separates a second order region from a first order one everywhere between D=4 and D=2. Our approach strongly suggests that the phase transitions that take place in physical membranes are of first order in agreement with most recent numerical simulations.

arXiv comment5 pages, 3 figures

References in corpus (29)

• The structure of suspended graphene sheets
• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Aspects of the Functional Renormalisation Group
• 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
• Optimization of the derivative expansion in the nonperturbative renormalization group
• 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
• Suppression of anharmonicities in crystalline membranes by external strain
• Graphene as a Prototype Crystalline Membrane
• Heisenberg frustrated magnets: a nonperturbative approach
• 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
• Thermal fluctuations of free standing graphene
• First-order transition of tethered membranes in 3d space
• XY frustrated systems: continuous exponents in discontinuous phase transitions
• Randomly dilute Ising model: A nonperturbative approach
• First-order phase transition in the tethered surface model on a sphere
• Nonlocal effective average action approach to crystalline phantom membranes
• High Precision Fourier Monte Carlo Simulation of Crystalline Membranes
• First-order phase transition of fixed connectivity surfaces
• Crumpling transition of the discrete planar folding in the negative-bending-rigidity regime
• Possible effects of tilt order on phase transitions of a fixed connectivity surface model

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• Thermodynamics of quantum crystalline membranes
• A glassy phase in quenched disordered graphene and crystalline membranes
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• The flat phase of quantum polymerized membranes
• Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets
• Thermal buckling transition of crystalline membranes in a field
• 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
• Wrinkling transition in quenched disordered membranes at two loops
• Spontaneous symmetry breaking and the flat phase of crystalline membranes
• Finsler geometry modeling of phase separation in multi-component membranes
• Interplay of topology and geometry in frustrated 2d Heisenberg magnets
• Universal behaviors in the wrinkling transition of disordered membranes
• Flat phase of quenched disordered membranes at three-loop order
• Optimized regulator for the quantized anharmonic oscillator
• Effective models of membranes from symmetry breaking
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• Parallel tempering Monte Carlo simulations of spherical fixed-connectivity model for polymerized membranes
• Dependence of the surface tension on the shape of surface boundary
• Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling
• Surface tension of membranes depending on the boundary shape
• Geometric control of tilt transition dynamics in single-clamped thermalized elastic sheets
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order
• Renormalization group approach to the elastic properties of graphene bilayers