In many biological processes, such as wound healing, cell tissues undergo an epithelial-to-mesenchymal transition, which is a transition from a more rigid to a more fluid state. Here, we investigate the solid/fluid transition of cell tissues within the framework of the self-propelled Voronoi model, which accounts for the deformability of the cells, for their many-body interactions, and for their polarized motility. The transition is controlled by two parameters, respectively accounting for the strength of the self-propelling force of the cells, and for the mechanical rigidity of the cells. We find the melting transition to occur via a continuous solid-hexatic transition followed by a continuous hexatic-liquid transition, as in the Kosterlitz, Thouless, Halperin, Nelson, and Young scenario. This finding indicates that the hexatic phase may have an unexpected biological relevance.
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