Order parameter fluctuations in percolation: Application to nuclear multifragmentation

TL;DR

This paper investigates order parameter fluctuations in a 3D bond percolation model to identify the critical point with minimal finite-size effects, offering a practical approach for studying nuclear multifragmentation.

Contribution

It introduces a robust method to locate the percolation critical point using cumulant ratios, effective even for very small systems and applicable to nuclear clusterization phenomena.

Findings

Cumulant ratios reveal features near the percolation transition.

The critical point can be estimated without system size variation.

Finite-size effects are minimal, making the method practical for small systems.

Abstract

Order parameter fluctuations (the largest cluster size distribution) are studied within a three-dimensional bond percolation model on small lattices. Cumulant ratios measuring the fluctuations exhibit distinct features near the percolation transition (pseudocritical point), providing a method for its identification. The location of the critical point in the continuous limit can be estimated without variation of the system size. This method is remarkably insensitive to finite-size effects and may be applied even for a very small system. The possibility of using various measurable quantities for sorting events makes the procedure useful in studying clusterization phenomena, in particular nuclear multifragmentation. Finite-size scaling and delta-scaling relations are examined. The model shows inconsistency with some of the delta-scaling expectations. The role of surface effects is evaluated by comparing results for free and periodic boundary conditions.