Multifractality in Rotational Percolation Models

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.