Percolation of the aligned dimers on a square lattice

TL;DR

This study investigates how the orientation of dimers affects percolation thresholds and electrical conductivity on a square lattice, revealing lower thresholds for dimers than monomers and the universality class of the percolation process.

Contribution

It introduces a model analyzing anisotropic dimer deposition on a lattice, highlighting the impact of alignment on percolation thresholds and conductivity, extending understanding of anisotropic conductor properties.

Findings

Percolation threshold for dimers is lower than for monomers.

Isotropic dimer orientation yields the lowest percolation threshold (pc=0.562).

Dimer alignment influences electrical conductivity behavior.

Abstract

Percolation and jamming phenomena are investigated for anisotropic sequential deposition of dimers (particles occupying two adjacent adsorption sites) on a square lattice. The influence of dimer alignment on the electrical conductivity was examined. The percolation threshold for deposition of dimers was lower than for deposition of monomers. Nevertheless, the problem belongs to the universality class of random percolation. The lowest percolation threshold (pc = 0.562) was observed for isotropic orientation of dimers. It was higher (pc = 0.586) in the case of dimers aligned strictly along one direction. The state of dimer orientation influenced the concentration dependence of electrical conductivity. The proposed model seems to be useful for description of the percolating properties of anisotropic conductors.