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

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)

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

References in corpus (1)

• Critical and Topological Properties of Cluster Boundaries in the $3d$ Ising Model