Multifractality in Rotational Percolation Models

TL;DR

This paper investigates the multifractal properties of rotationally constrained percolation models by introducing a state variable that counts site visits, providing a new approach that does not rely on external probes.

Contribution

It proposes a novel method to study multifractality in percolation clusters using a state variable, avoiding external agents like currents or walkers.

Findings

Identifies multifractal nature of clusters under rotational constraints

Defines measures based on site visit counts for analysis

Classifies the universality of these models

Abstract

In rotationally constrained percolation models, a site of a percolation cluster could be occupied more than once from different directions due to the nature of the rotational constraint. A state variable $s_i$ is assigned to each lattice site whose value corresponds to the number times it has been visited during the growth of a cluster. It is proposed here that the percolation transition and the multifractal aspects of infinite percolation clusters under rotational constraint can be studied defining suitable measures in terms of the state variable $s_i$. This method does not require to introduce any external agency like an electric current or a random walker in order to explore multifractality as in the case of ordinary percolation. The state variable representation also describes the universality class of the percolation models appropriately.