Reevaluation of series expansions for roughening transitions

Ninth-order low-temperature series expansions for the Ising interface and SOS (solid on solid) models were once thought to be a suitable method for determining the location and exponents of the roughening transition. However, the temperature and exponent estimates thus derived were found to fail to obey exact, rigorous inequalities derived by Swendsen from Lapunov inequalities, and this led to obvious doubts as to the reliability of the estimates from such short series. In this Rapid Communication I show that a careful reanalysis of the series gives temperature and central-exponent estimates that obey the Swendsen-Lapunov inequalities, and are in excellent agreement with Monte Carlo and renormalization-group estimates. This reanalysis gives the first reliable estimate of the difference in the Ising interface and SOS roughening temperatures, within the same approximation. I find $Y_R\left(\mathrm{I}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\right)=0.199\mathrm{}\pm 0.010$ [$T_R\left(\mathrm{Ising}\right)=2.475\mathrm{}\pm 0.075$], and $Y_R\left(\mathrm{SOS}\right)=0.207\mathrm{}\pm 0.009$ [$T_r\left(\mathrm{SOS}\right)=2.54\mathrm{}\pm 0.07$].