Geometry of fully coordinated, two-dimensional percolation

TL;DR

This paper investigates the geometric properties of critical clusters in fully coordinated 2D percolation, revealing static universality with ordinary percolation but differences in dynamic behavior due to interior site distributions.

Contribution

It provides the first detailed comparison of static and dynamic exponents in fully coordinated 2D percolation, highlighting differences from ordinary percolation.

Findings

Static exponents match ordinary percolation

Dynamic exponents differ from ordinary percolation

Interior site distribution impacts dynamic behavior

Abstract

We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same universality class with ordinary percolation statically but not so dynamically. We show that there are large differences in the number and distribution of the interior sites between the two problems which may account for the different dynamic nature.