Fourier Monte Carlo simulation of crystalline membranes in the flat phase

24th IUPAP Conference on Computational Physics

物理学;计算机科学

Tröster, Andreas^1

Vienna University of Technology, Wiedner Hauptstrasse 8-10/136, A-1040 Wien, Austria^1

关键词: Correlation function;    Critical slowing down;    Effective Hamiltonian;    Finite size effect;    Finite-size scaling analysis;    Mean squared displacement;    Out-of-plane deformations;    Statistical accuracy;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/454/1/012032/pdf
DOI  :  10.1088/1742-6596/454/1/012032

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

Stimulated by the recent interest in graphene, the elastic behavior of crystalline membranes continues to be under debate. In their flat phase, one observes scaling of the correlation functions of in-plane and out-of-plane deformations u(x) and f(x) at long wavelengths with respect to a given reference plane governed by a single universal exponent η. The purpose of the present article is to explain the ideas and techniques underlying our Fourier Monte Carlo simulation approach to the numerical determination of η in much greater detail than was possible in a recent letter that is currently under review. Our simulations are based on an effective Hamiltonian first derived by Nelson and Peliti formulated exclusively in terms of the Fourier amplitudes (q) of the field f(x), and we calculate the out-of-plane correlation function |(q)|2(q) and their related mean squared displacement (Δf)2. The key to the progress reported in this work is the observation that on tuning the Monte Carlo acceptance rates separately for each wave vector, we are able to eliminate critical slowing down and thus achieve unprecedented statistical accuracy. A finite size scaling analysis for (Δf)2gives η = 0.795(10). In the alternative approach, where we study the scaling of (q), we observe an unexpected anisotropic finite size effect at small wave vectors which hampers a similarly accurate numerical analysis.