Postprocessing techniques for gradient percolation predictions on the square lattice

Area of Science:

• Statistical Physics
• Computational Science

Background:

• Site percolation on regular lattices is a fundamental problem in statistical physics.
• Previous studies assumed a linear relationship between probability gradients and percolation thresholds.

Purpose of the Study:

• To investigate the impact of quantization bias errors on percolation threshold predictions.
• To propose a mitigation strategy for these errors.
• To challenge the linearity assumption in percolation threshold analysis.

Main Methods:

• Extensive computational experiments were conducted.
• Analysis of occupation probability distributions.
• Identification and evaluation of alternative convergence metrics.

Main Results:

• The assumed linear relationship between probability gradient and percolation threshold is invalid.
• Average occupation probabilities do not monotonically converge to the true percolation threshold due to distribution skewness.
• Several alternative metrics demonstrate monotonic convergence.

Conclusions:

• Quantization bias significantly affects percolation threshold predictions, invalidating linear assumptions.
• New metrics are identified for more reliable percolation threshold estimation in the presence of bias.
• This work provides a refined understanding of percolation phenomena under computational constraints.