The Interface Tension of the 3-Dimensional Ising Model in the Scaling Region

Using the Monte Carlo method, we determine the free energy of the interface of the 3D Ising model in the scaling region. By integrating the interface energies over the inverse temperature $\beta$, we obtain estimates for the free energies of interfaces with cross sections up to 96 by 96, and for a range $0.223 \leq \beta \leq 0.23$. Our data yield a precise estimation of the interface tensions $\sigma$. We determine the amplitude $\sigma_0$ in the critical law $\sigma \sim \sigma_0 t^{\mu}$ and estimate the combination $\sigma \xi^2$ which yields the universal constant $R_{-}$ in the critical limit.