1993/04/21 by Vladimir S. Dotsenko, V. Dotsenko, Paul Windey +9 · 1 citation
Mathematics · Physics and Astronomy · #Cluster (spacecraft) #Combinatorics #Complex Network Analysis Techniques #Condensed matter physics #Ising model #Mathematics #Percolation (cognitive psychology) #Physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevlett.71.811
published as Phys.Rev.Lett. 71 (1993) 811-814 · REVISED NOW NO APS MACROS NEEDED FOR HEPTH USERS 4 p 4 f, EFI 93-24
arxiv created 1993/04/21 · openalex publication_date 1993/08/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the ensemble of surfaces surrounding critical clusters at T=Tc in the 3D Ising model. We find that Ng(A), the number of surfaces of genus g and area A, behaves as Ax(g)e^\mathrm\ensuremath-\mathrm\ensuremathμA. We show that \ensuremathμ is constant and x(g) is approximately linear; the sum tsumg Ng(A) scales as a power of A. The cluster volume is proportional to its surface area. We discuss similar reuslts for the ordinary spin clusters of the 3D Ising model and for 3D bond percolation.