Capillary Waves in Binder's Approach to the Interface Tension

Abstract

In Binder's approach the reduced interface tension sigma of the Ising model in the broken phase is determined from the finite volume effects of the partition function Z(M) at fixed total magnetization M. For small |M| the partition function of a system of size L^d with periodic boundary conditions is dominated by configurations with two interfaces, such that Z(M) ~ exp(- 2 sigma L^{d-1}). Capillary wave fluctuations of the interfaces correct this result to Z(M) ~ exp(- 2 sigma L^{d-1}) with x = -1. The knowledge of the pre-exponential behavior allows an improved fit of numerical data, and a determination of the interface stiffness.