Bond percolation in distorted simple cubic and body-centered cubic lattices

TL;DR

This study explores how structural distortions in cubic lattices affect bond percolation thresholds, revealing complex relationships between geometric disorder and connectivity through extensive Monte Carlo simulations.

Contribution

It introduces a novel approach by coupling geometric disorder with connectivity via a connection threshold, analyzing its impact on percolation in 3D lattices.

Findings

Percolation threshold increases with distortion when threshold exceeds original nearest-neighbor distance.

Monotonic behavior of thresholds breaks down below the original nearest-neighbor distance.

Identifies critical thresholds for global spanning under various distortion and connection conditions.

Abstract

We investigate the effect of structural distortion on bond percolation in simple cubic and body-centered cubic lattices using extensive Monte Carlo simulations. Distortion is introduced through controlled random displacements of lattice sites, thereby modifying nearest-neighbor distances. Bond occupation is permitted only when the bond length is smaller than a prescribed connection threshold, directly coupling geometric disorder to connectivity. Finite-size scaling analysis is employed to determine percolation thresholds for finite systems and in the thermodynamic limit. We find that when the connection threshold exceeds the nearest-neighbor distance of the undistorted lattice, the percolation threshold increases monotonically with distortion strength, indicating a systematic suppression of spanning. In contrast, this monotonic behavior breaks down when the connection threshold is below the nearest-neighbor distance of the undistorted lattice, highlighting a nontrivial interplay between geometric distortion and connectivity. We further identify critical values of the connection threshold and the distortion amplitude required for global spanning when all the allowed bonds are occupied. All qualitative behaviors remain robust across both lattice geometries. These results clarify how geometric disorder reshapes percolation in three-dimensional crystalline networks.