Percolation threshold and critical exponent analysis in equilibrium systems on simple cubic and BCC lattices

Abstract

Simulations using the Monte Carlo method were performed with Kawasaki dynamics at atemperature of 300 K, evaluating the percolation threshold (the fraction of occupied sitesnecessary for the system to percolate). Three different percolation criteria were considered:𝑅 𝑈 (percolation in at least one of the x, y, or z directions), 𝑅 𝐼 (simultaneous percolation in allthree directions), and 𝑅 𝐴 (average of the percolation probabilities in each direction). The resultsshow how the percolation threshold varies with the interaction between particles (representedby the parameter 𝐽 ). It was observed that repulsive interactions (𝐽 > 0) increase the percolationthreshold, while attractive interactions (𝐽 < 0) reduce it. For large values of 𝐽 , the percolationthreshold curves stabilize at certain limits.