Percolation in a reduced equilibrium model of planar cell polarity

Planar cell polarity (PCP) is a biological phenomenon where a large number of cells get polarized and coordinatedly align in a plane. PCP is an example of self-organization through local and global interactions between cells. In this work, we have used a lattice-based spin model for PCP that mimics the alignment of cells through local interactions. We have investigated the equilibrium behavior of this model. In this model, alignment of cells leads to the formation of clusters of aligned cells, and such clustering exhibits percolation transition. Even though the alignment of a cell in this model depends upon its neighbors, finite-size scaling analysis shows that this model belongs to the universality class of simple two-dimensional random percolation.