Percolation in the Harmonic Crystal and Voter Model in three dimensions

Details Percolation in the Harmonic Crystal and Voter Model in three dimensions Percolation in the Harmonic Crystal and Voter Model in three dimensions

2006-01-06

arxiv.org/abs/cond-mat/0601108v3

Physics

Condensed Matter

Statistical Mechanics

8 figures. new version significantly different from the old one, includes new results, figures etc

Scientific paper

10.1103/PhysRevE.74.031120

We investigate the site percolation transition in two strongly correlated systems in three dimensions: the massless harmonic crystal and the voter model. In the first case we start with a Gibbs measure for the potential, $U=\frac{J}{2} \sum_{} (\phi(x) - \phi(y))^2$, $x,y \in \mathbb{Z}^3$, $J > 0$ and $\phi(x) \in \mathbb{R}$, a scalar height variable, and define occupation variables $\rho_h(x) =1,(0)$ for $\phi(x) > h (

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