High Precision Fourier Monte Carlo Simulation of Crystalline Membranes

Abstract

We report an essential improvement of the plain Fourier Monte Carlo algorithm that promises to be a powerful tool for investigating critical behavior in a large class of lattice models, in particular those containing microscopic or effective long-ranged interactions. On tuning the Monte Carlo acceptance rates separately for each wave vector, we are able to drastically reduce critical slowing down. We illustrate the resulting efficiency and unprecedented accuracy of our algorithm with a calculation of the universal elastic properties of crystalline membranes in the flat phase and derive a numerical estimate eta = 0.795(10) for the critical exponent eta that challenges those derived from other recent simulations. The large system sizes accessible to our present algorithm also allow to demonstrate that insufficiently taking into account corrections to scaling may severely hamper a finite size scaling analysis. This observation may also help to clarify the apparent disagreement of published numerical estimates of eta in the existing literature.

7 pages, 6 figures, accepted for publication by Phys. Rev. B (2013)

References in corpus (4)

• Scaling Properties of Flexible Membranes from Atomistic Simulations: Application to Graphene
• Crumpling transition and flat phase of polymerized phantom membranes
• Thermal fluctuations of free standing graphene
• Nonlocal effective average action approach to crystalline phantom membranes

Cited by in corpus (22)

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• Thermal crumpling of perforated two-dimensional sheets
• Scaling behavior of crystalline membranes: an $\epsilon$-expansion approach
• The flat phase of polymerized membranes at two-loop order
• Thermal stiffening of clamped elastic ribbons
• Three-loop order approach to flat polymerized membranes
• Universal behavior of crystalline membranes: crumpling transition and Poisson ratio of the flat phase
• Fourier Monte Carlo Renormalization Group Approach to Crystalline Membranes
• Spontaneous tilt of single-clamped thermal elastic sheets
• Elastic properties and mechanical stability of bilayer graphene: Molecular dynamics simulations
• Vibrations and tunneling of strained nanoribbons at finite temperature
• Four-loop critical properties of polymerized membranes
• Thermally driven elastic membranes are quasi-linear across all scales
• Stiffening Thermal Membranes by Cutting
• Flat polymerized membranes at three-loop order
• Effective models of membranes from symmetry breaking
• Renormalization group approach to the elastic properties of graphene bilayers