Shape-dependent universality in percolation
Robert M. Ziff (1), Christian D. Lorenz (1), and Peter Kleban (2) ((1), University of Michigan, (2) University of Maine)
TL;DR
This paper explores how the shape and boundary conditions of a torus influence the universal properties of percolation, revealing shape-dependent universality classes.
Contribution
It demonstrates that universality in percolation depends on both aspect ratio and boundary twists, extending understanding of boundary effects in percolation models.
Findings
Universality class depends on boundary twist and aspect ratio.
Excess cluster number varies with shape and boundary conditions.
Boundary conditions influence percolation properties on a torus.
Abstract
The shape-dependent universality of the excess percolation cluster number and cross-configuration probability on a torus is discussed. Besides the aspect ratio of the torus, the universality class depends upon the twist in the periodic boundary conditions, which for example are generally introduced when triangular lattices are used in simulations.
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