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Abstract: We calculate mean square deviations for crystals in one and two dimensions.For the two dimensional lattices, we consider several distinct geometries i.e.square, triangular, and honeycomb, and we find the same essential phenomenafor each lattice structure. We investigate the stability of long-rangecrystalline order for a variety of coupling schemes, including short-rangeexponentially decaying inter-atomic potentials and long-range interactions witha power law dependence r^{-alpha}. For the latter in the 1D case, we find acritical value alpha c1D = 1.615 +- 0.005 for the power law decay exponentbelow which crystalline order is intact, and above which thermal fluctuationsdestroy long-range order when T > 0. The corresponding critical value for twodimensional lattices with displacements confined to the plane is alpha c2D =3.15 +- 0.025. If motion perpendicular to the crystal plane is permitted,thermally induced distortions diverge rapidly i.e. linearly in dual layersystems with local stiffness provided by an extended coupling scheme, even ifthe interaction is long ranged, decaying as a power law in the separationbetween lattice sites.



Autor: D. J. Priour Jr

Fuente: https://arxiv.org/







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