New critical frontiers for the Potts and percolation models

TL;DR

This paper determines critical thresholds for various Potts and percolation models on dual-structure lattices, extending previous results to broader models and lattice types.

Contribution

It generalizes existing threshold calculations for percolation models to include Potts models and a wider class of lattices using duality methods.

Findings

Critical thresholds for Potts and percolation models on specific lattices are established.

The results extend previous thresholds from martini lattices to more general lattice structures.

Duality considerations are key to deriving these thresholds.

Abstract

We obtain the critical threshold for a host of Potts and percolation models on lattices having a structure which permits a duality consideration. The consideration generalizes the recently obtained thresholds of Scullard and Ziff for bond and site percolation on the martini and related lattices to the Potts model and to other lattices.