NPAC Technical Report SCCS-600
The Phenomenology of Strings and Clusters in the 3-d Ising Model
Vladimir Dotsenko, Marco Picco, Paul Windey, Geoffrey Harris, Enzo Marinari, Emil Martinec
Submitted January 1 1994
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)