Abstract
Recent computer simulations have stressed the dependence of transport properties on boundary conditions in two dimensions, where fluctuations and boundary conditions are equally important effects of order N1/2. Elastically isotropic harmonic crystals provide a test case in which these two effects can be studied precisely without sacrificing realism. We investigate the boundary dependence of spatial fluctuations in two-dimensional crystals. Our results confirm the expected boundary independence of the extensive vibrational entropy. We find also that clamped crystal boundaries significantly alter the rate of divergence of the root-mean-square (rms) displacement with crystal size, but do not alter the [logarithmic] functional form, which is known to dominate vibrational fluctuations in periodic two-dimensional crystals.
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