1. The Phenomenology of Strings and Clusters in the 3d Ising Model
- Author
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Dotsenko, Vladimir S., Picco, Marco, Windey, Paul, Harris, Geoffrey R., Marinari, Enzo, Emil Martinec, Laboratoire de Physique Théorique et Hautes Energies (LPTHE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Physics Department (Physics Department), Syracuse University, Department of Physics [Chicago], University of Chicago, Dipartimento di Fisica (Dipartimento di Fisica), Università degli Studi di Cagliari = University of Cagliari (UniCa), NATO ASI Series, and Universita degli Studi di Cagliari [Cagliari]
- Subjects
High Energy Physics - Theory ,High Energy Physics - Lattice ,High Energy Physics - Theory (hep-th) ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,Condensed Matter (cond-mat) ,High Energy Physics - Lattice (hep-lat) ,FOS: Physical sciences ,Condensed Matter - Abstract
We examine the geometrical and topological properties of surfaces surrounding clusters in the 3--$d$ 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. 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 $\tau \sim 2.2$. We address the prospects for a string--theoretic description of cluster boundaries. (To appear in proceedings for the Cargese Workshop on "String Theory, Conformal Models and Topological Field Theories", May 1993), Comment: 20 pages followed by 15 uuencoded ps figures, latex, SU-HEP-4241-563, PAR-LPTHE 93/59
- Published
- 1995