Universality in boundary domain growth by sudden bridging

TL;DR

This paper demonstrates that boundary domain growth in cluster aggregation at maximum concentration exhibits universal scaling behavior, with the boundary interface width's maximum scaling as L to the power of 1, regardless of the specific model.

Contribution

It reveals a universal scaling law for boundary domain growth in cluster aggregation at maximum concentration, independent of the specific percolation model used.

Findings

Boundary interface width scales as L^1 at maximum concentration.

Universal behavior observed across different cluster percolation models.

Rapid boundary growth occurs at the percolation threshold, leading to universal scaling.

Abstract

We report on universality in boundary domain growth in cluster aggregation in the limit of maximum concentration. Maximal concentration means that the diffusivity of the clusters is effectively zero and, instead, clusters merge successively in a percolation process, which leads to a sudden growth of the boundary domains. For two-dimensional square lattices of linear dimension L, independent of the models studied here, we find that the maximum of the boundary interface width, the susceptibility $\chi$, exhibits the scaling $\chi \sim L^{\gamma}$ with the universal exponent $\gamma = 1$. The rapid growth of the boundary domain at the percolation threshold, which is guaranteed to occur for almost {\em any} cluster percolation process, underlies the universal scaling of $\chi$.