The Interface Tension of the Three-dimensional Ising Model in Two-loop Order

Abstract

In liquid mixtures and other binary systems at low temperatures the pure phases may coexist, separated by an interface. The interface tension vanishes according to $\sigma = \sigma_0 (1 - T/T_c)^{\mu}$ as the temperature T approaches the critical point from below. Similarly the correlation length diverges as $\xi = f_- (1 - T/T_c)^{-\nu}$ in the low temperature region. For three-dimensional systems the dimensionless product $R_- = \sigma_0 f_-^2$ is universal. We calculate its value in the framework of field theory in d=3 dimensions by means of a saddle-point expansion around the kink solution including two-loop corrections. The result R_ = 0.1065(9), where the error is mainly due to the uncertainty in the renormalized coupling constant, is compatible with experimental data and Monte Carlo calculations.