SELF-AVOIDING SURFACES IN THE 3D ISING-MODEL

We examine the geometrical and topological properties of surfaces surr ounding clusters in the 3d Ising model, For geometrical clusters at th e percolation temperature and Fortuin-Kasteleyn clusters at T-c, the n umber of surfaces of genus g and area A behaves as A(x(g)) e(-mu(g)A), with x approximately linear in g and mu constant, These scaling laws are the same as those we obtain for simulations of 3d bond percolation . We observe that cross sections of spin domain boundaries at T-c deco mpose into a distribution N(1) of loops of length I that scales as l(- tau) with tau similar to 2.2. We also present some new numerical resul ts for 2d self-avoiding loops that we compare with analytic prediction s, We address the prospects for a string-theoretic description of clus ter boundaries.