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We propose a continuum model of percolation in two dimensions for overlappingdisks with spin. In this model the existence of bonds is determined by thedistance between the centers of the disks, and by the scalar product of the(randomly) directed spin with the direction of the vector connecting thecenters of neighboring disks. The direction of a single spin is controlled by a"temperature", representing the amount of polarization of the spins in thedirection of an external field. Our model is inspired by biological neuronalnetworks and aims to characterize their topological properties when axonalguidance plays a major role. We numerically study the phase diagram of themodel observing the emergence of a giant strongly connected component,representing the portion of neurons that are causally connected. We providestrong evidence that the critical exponents depend on the temperature.

Emergence of strongly connected giant components in continuum disk-spin percolation