The Phenomenology of Strings and Clusters in the 3-d Ising Model

Details The Phenomenology of Strings and Clusters in the 3-d Ising Model The Phenomenology of Strings and Clusters in the 3-d Ising Model

1994-01-26

arxiv.org/abs/hep-th/9401129v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages followed by 15 uuencoded ps figures, latex, SU-HEP-4241-563, PAR-LPTHE 93/59

Scientific paper

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)

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