2001/11/30 by Louis-Pierre Arguin, Louis‐Pierre Arguin · 1 citation
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Biochemistry #Chemistry #Enzyme #Gene #Geometry #Homology (biology) #Homology modeling #Mathematics #Theoretical and Computational Physics #Topological and Geometric Data Analysis #Torus #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1023/a:1019979326380
published as J.Statist.Phys.109:301-310,2002 · 12 pages, 2 figures, submitted to J. Stat. Phys
arxiv created 2002/05/17 · openalex publication_date 2002/10/01 · arxiv updated 2010/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Topological properties of Fortuin-Kasteleyn clusters are studied on the torus. Namely, the probability that their topology yields a given subgroup of the first homology group of the torus is computed for Q=1, 2, 3 and 4. The expressions generalize those obtained by Pinson for percolation (Q=1). Numerical results are also presented for three tori of different moduli. They agree with the theoretical predictions for Q=1, 2 and 3. For Q=4 agreement is not ruled out but what seems logarithmic corrections makes it harder to decide.