On the field-dependence of eigenvalues of correlation function matrices H and C in the fluctuating interface of the two-dimensional SOS model

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Abstract
The density-density correlation function matrix H(z1,z2;x) and its Fourier transform H(z1,z2;k) in the interface of a lattice gas in the solid-on-solid (SOS) approximation were computed numerically with the aid of the transfer matrix. Strips zmax* infinity were studied in a weak external field. The matrices H and H were diagonalised for small kperpendicular to and for kperpendicular to =0. As postulated by Wertheim, the largest (single) eigenvalue of H(kperpendicular to =0) was well separated from the others, but its field dependence was represented by lambda H-1=A( beta V0)delta with delta =0.75 or delta =1 for alpha =2 or alpha =1 respectively, with alpha specifying the power law of the external field.

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