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Abstract: We study the percolation properties of the growing clusters model. In thismodel, a number of seeds placed on random locations on a lattice are allowed togrow with a constant velocity to form clusters. When two or more clusterseventually touch each other they immediately stop their growth. The modelexhibits a discontinuous transition for very low values of the seedconcentration $p$ and a second, non-trivial continuous phase transition forintermediate $p$ values. Here we study in detail this continuous transitionthat separates a phase of finite clusters from a phase characterized by thepresence of a giant component. Using finite size scaling and large scale MonteCarlo simulations we determine the value of the percolation threshold where thegiant component first appears, and the critical exponents that characterize thetransition. We find that the transition belongs to a different universalityclass from the standard percolation transition.



Author: Nikolaos Tsakiris, Michail Maragakis, Kosmas Kosmidis, Panos Argyrakis

Source: https://arxiv.org/







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