Breakdown of Universality in Directed Spiral Percolation

TL;DR

This study investigates directed spiral percolation (DSP) on 2D lattices, revealing that critical properties differ significantly between square and triangular lattices, indicating a breakdown of universality in this model.

Contribution

It demonstrates that DSP exhibits non-universal behavior across different lattice types, contrasting with traditional percolation models.

Findings

Clusters are more compact on the triangular lattice.

Critical exponents differ significantly between lattices.

DSP shows breakdown of universality in 2D.

Abstract

Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated in this model are generally rarefied and have chiral dangling ends on both the square and triangular lattices. It is found that the clusters are more compact and less anisotropic on the triangular lattice than on the square lattice. The elongation of the clusters is in a different direction than the imposed directional constraint on both the lattices. The values of some of the critical exponents and fractal dimension are found considerably different on the two lattices. The DSP model then exhibits a breakdown of universality in 2D between the square and triangular lattices. The values of the critical exponents obtained for the triangular lattice are not only different from that of the square lattice but also different form other percolation models.