Studies in random surfaces

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




Mark Bowick


crystalline, screening approximation, flat phase, Monte Carlo, surface science

Subject Categories

Condensed Matter Physics | Physics


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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