Title
Studies in random surfaces
Date of Award
1997
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Physics
Advisor(s)
Mark Bowick
Keywords
crystalline, screening approximation, flat phase, Monte Carlo, surface science
Subject Categories
Condensed Matter Physics | Physics
Abstract
Crystalline surfaces model important experimental and biological systems. With the insight provided by theoretical analyses of the model, we study the behavior of a crystalline surface in the flat phase, using Monte Carlo simulations. The flat phase is characterized by the anomalous scaling of the coupling constant. We extract the scaling exponents from the finite size scaling of the correlation functions, and we compare our results to the analytical predictions and to previous numerical determinations. At bending rigidity $\kappa=1.1,$ we find $\nu=0.95(5)$ (Hausdorff dimension $d\sb{H}=2/\nu=2.1(1)),\ \zeta=0.64(2)$ and $\eta\sb{u}=0.50(1).$ These results are consistent with the scaling relation $\zeta=(2+\eta\sb{u})/4.$ The additional scaling relation $\eta=2(1-\zeta)$ implies $\eta=0.72(4).$ A direct measurement of $\eta$ from the power-law decay of the normal-normal correlation function yields $\eta\approx0.6$ on the 128$\sp2$ lattice. We also measure the Poisson ratio $\sigma$ using a fluctuation-dissipation argument. The precise numerical value we find is a $\sigma\simeq{-}0.32$ on a 128$\sp2$ lattice at bending rigidity $\kappa=1.1.$ This is in excellent agreement with the prediction $\sigma={-}1/3$ following from the self-consistent screening approximation of Le Doussal and Radzihovsky. Finally, we discuss some details of the Monte Carlo methods.
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Recommended Citation
Falcioni, Falcioni, "Studies in random surfaces" (1997). Physics - Dissertations. 86.
https://surface.syr.edu/phy_etd/86
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