Asymptotic behaviour of correlation functions and the interfacial tension in the two-dimensional SOS model of an interface in zero external field

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Abstract
The modified direct correlation functions Ccond and Csym are studied for a two-dimensional SOS system (M* infinity ) in a zero external field G identical to 0. The asymptotic limit W to infinity of the interface width W=(M+1)/ pi is considered in particular, also in connection with the Yvon-Triezenberg-Zwanzig (YTZ) formula for the interfacial tension Gamma and with its modification obtained by Ciach et al (1987). The successive contributions to the interfacial tension Gamma , resulting from various terms of the derived relations, are computed and discussed. In the asymptotic limit W to infinity the interfacial tensions obtained from the YTZ formula and from the Ciach formula agree with each other and with Gamma calculated earlier by Evans (1979) and extrapolated to G=0 by Stecki and Dudowicz (1985).