1995/04/14 by Vladimir S. Dotsenko, Vl. S Dotsenko, G. Harris +9 · 1 citation
Mathematics · Physics and Astronomy · #Cluster (spacecraft) #Complex Network Analysis Techniques #Computer science #Condensed matter physics #Distribution (mathematics) #Domain (mathematical analysis) #Domain wall (magnetism) #Electrical resistivity and conductivity #Geometry #Ising model #Ising spin #Magnetization #Mathematical analysis #Mathematical physics #Mathematics #Percolation (cognitive psychology) #Percolation threshold #Physics #Quantum mechanics #Scaling #Statistical physics #Stochastic processes and statistical mechanics #String (physics) #Theoretical and Computational Physics #cond-mat #hep-lat #hep-th
paper · pdf · doi:10.1016/0550-3213(95)00278-z
published as Nucl.Phys. B448 (1995) 577-620 · latex file, followed by 34 ps figures (no epsf)
arxiv created 1995/04/14 · openalex publication_date 1995/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Tc, the number of surfaces of genus g and area A behaves as Ax(g) e−μ(g)A, with x approximately linear in g and μ 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 Tc decompose into a distribution N(l) of loops of length l that scales as l−τ with τ ∼ 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.