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.