Statistics of percolating clusters in a model of photosynthetic bacteria

In photosynthetic organisms the energy of the illuminating light is absorbed by the antenna complexes and transmitted by the excitons to the reaction centers (RCs). The energy of light is either absorbed by the RCs, leading to their ``closing'' or is emitted through fluorescence. The dynamics of the light absorption is described by a simple model developed for exciton migration that involves the exciton hopping probability and the exciton lifetime. During continuous illumination the fraction of closed RCs $x$ continuously increases, and at a critical threshold ${x}_{c}$, a percolation transition takes place. Performing extensive Monte Carlo simulations, we study the properties of the transition in this correlated percolation model. We measure the spanning probability in the vicinity of ${x}_{c}$, as well as the fractal properties of the critical percolating cluster, both in the bulk and at the surface.