FLUID INTERFACES IN THE 3D ISING-MODEL AS A DILUTE GAS OF HANDLES

We study the topology of fluid interfaces in the 3D Ising model in the rough phase. It turns out that such interfaces are accurately describ ed as dilute gases of microscopic handles, and the stiffness of the in terface increases with the genus. The number of configurations of genu s g follows a Poisson-like distribution. The probability per unit area for creating a handle is well fitted in a wide range of the inverse t emperature beta near the roughening point by an exponentially decreasi ng function of beta. The procedure of summing over all topologies resu lts in an effective interface whose squared width scales logarithmical ly with the lattice size.