Extended Capillary Waves and the Negative Rigidity Coefficient in the d=2 SOS model

Details Extended Capillary Waves and the Negative Rigidity Coefficient in the d=2 SOS model Extended Capillary Waves and the Negative Rigidity Coefficient in the d=2 SOS model

2006-02-15

arxiv.org/abs/cond-mat/0602365v1

Physics

Condensed Matter

Soft Condensed Matter

file.tex plus 4 (four) figures in Postscript

Scientific paper

10.1103/PhysRevB.74.033409

The solid-on-solid (SOS) model of an interface separating two phases is exactly soluble in two dimensions (d=2) when the interface becomes a one-dimensional string. The exact solution in terms of the transfer matrix is recalled and the density-density correlation function $H(z_1,z_2;\Delta x)$ together with its projections, is computed. It is demonstrated that the shape fluctuations follow the (extended) capillary-wave theory expression $S(q)=kT/(D+\gamma q^2 +\kappa q^4) $ for sufficiently small wave vectors $q$. We find $\kappa$ {\it negative}, $\kappa <0$ . At $q=2\pi$ there is a strong nearest-neighbor peak. Both these results confirm the earlier findings as established in simulations in d=3 and in continuous space, but now in an exactly soluble lattice model.

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