Fourier Monte Carlo Renormalization Group Approach to Crystalline Membranes

Abstract

The computation of the critical exponent eta characterizing the universal elastic behavior of crystalline membranes in the flat phase continues to represent challenges to theorists as well as computer simulators that manifest themselves in a considerable spread of numerical results for eta published in the literature. We present new insight to this problem that results from combining Wilson's momentum shell renormalization group method with the power of modern computer simulations based on the Fourier Monte Carlo algorithm. After discussing the ideas and difficulties underlying this combined scheme, we present a calculation of the renormalization group flow of the effective 2d Young modulus for momentum shells of different thickness. Extrapolation to infinite shell thickness allows to produce results in reasonable agreement with those obtained by functional renormalization group or by Fourier Monte Carlo simulations in combination with finite size scaling. Moreover, our new method allows for the first time to obtain a decent estimate for the value of the Wegner exponent omega that determines the leading correction to scaling, which in turn allows to refine our numerical estimate for eta previously obtained from precise finite size scaling data.

arXiv commentPhys. Rev. E, in print

References in corpus (16)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Critical Phenomena and Renormalization-Group Theory
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Self-Consistent Theory of Polymerized Membranes
• The Statistical Mechanics of Membranes
• Scaling Properties of Flexible Membranes from Atomistic Simulations: Application to Graphene
• Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error
• Crumpling transition and flat phase of polymerized phantom membranes
• Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus
• The Flat Phase of Crystalline Membranes
• The Structure of Physical Crystalline Membranes within the Self-Consistent Screening Approximation
• Thermal fluctuations of free standing graphene
• Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals
• Nonlocal effective average action approach to crystalline phantom membranes
• High Precision Fourier Monte Carlo Simulation of Crystalline Membranes
• Renormalization Group Flow of Hexatic Membranes

Cited by in corpus (10)

• Non-Hookean statistical mechanics of clamped graphene ribbons
• Statistical mechanics of thin spherical shells
• Buckling of thermalized elastic sheets
• 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
• Spontaneous tilt of single-clamped thermal elastic sheets
• Stiffening Thermal Membranes by Cutting