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We examine the geometrical and topological properties of surfaces surrounding clusters in the 3d Ising model. For geometrical clusters at the percolation temperature and Fortuin-Kasteleyn clusters at T c , the number 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 decompose into a distribution N(l) of loops of length l that scales as l -$\tau$ with $\tau$ ∼ 2.2. We also present some new numerical results for 2d self-avoiding loops that we compare with analytic predictions. We address the prospects for a string-theoretic description of cluster boundaries. \textcopyright 1995.

@article{Dotsenko1995d, abstract = {We examine the geometrical and topological properties of surfaces surrounding clusters in the 3d Ising model. For geometrical clusters at the percolation temperature and Fortuin-Kasteleyn clusters at T c , the number 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 decompose into a distribution N(l) of loops of length l that scales as l -$\tau$ with $\tau$ ∼ 2.2. We also present some new numerical results for 2d self-avoiding loops that we compare with analytic predictions. We address the prospects for a string-theoretic description of cluster boundaries. {\textcopyright} 1995.}, author = {Dotsenko, V.S. VS and Picco, M. and Windey, P. and Harris, G. and Martinec, E. and Marinari, E.}, doi = {10.1016/0550-3213(95)00278-Z}, file = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko et al. - 1995 - Self-avoiding surfaces in the 3d Ising model(2).pdf:pdf}, issn = {05503213}, journal = {Nuclear Physics B}, number = {3}, pages = {577}, title = {{Self-avoiding surfaces in the 3d Ising model}}, url = {http://www.sciencedirect.com/science/article/pii/055032139500278Z}, volume = {488}, year = {1995} }

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