The emergence of clustering and coarsening in crowded ensembles of self-propelled agents is studied using a lattice model in one-dimension. The persistent exclusion process, where particles move at directions that change randomly at a low tumble rate $α$, is extended allowing sites to be occupied by more than one particle, with a maximum $n_\text{max}$ per site. Three phases are distinguished. For $n_\text{max}=1$ a gas of clusters form, with sizes distributed exponentially and no coarsening takes place. For $n_\text{max}\geq 3$ and small values of $α$, coarsening takes place and few large clusters appear, with a large fraction of the total number of particles in them. In the same range of $n_\text{max}$ but for larger values of $α$, a gas phase where a negligible fraction of particles takes part of clusters. Finally, $n_\text{max}=2$ corresponds to a crossover phase. The character of the transitions between phases is studied extending the model to allow $n_\text{max}$ to take real values and jumps to an occupied site are probabilistic. The transition from the gas of clusters to the coarsening phase is continuous and the mass of the large clusters grows continuously when varying the maximum occupancy, and the crossover found corresponds to values close to the transition. The second transition, from the coarsening to the gaseous phase can be either continuous or discontinuous depending on the parameters, with a critical point separating both cases.
Long-range correlations in a locally constrained exclusion process
University of Augsburg（奥格斯堡大学）；Instituto Superior Técnico, University of Lisbon（里斯本大学高级技术学院）；Laboratoire de Physique et Chimie Théoriques, University of Lorraine（洛林大学理论与物理化学实验室）
