  The size and shape of a large variety of polymeric particles, including
biological cells, star polymers, dendrimes, and microgels, depend on the
applied stresses as the particles are extremely soft. In high-density
suspensions these particles deform as stressed by their neighbors, which
implies that the interparticle interaction becomes of many-body type.
Investigating a two-dimensional model of cell tissue, where the single particle
shear modulus is related to the cell adhesion strength, here we show that the
particle deformability affects the melting scenario. On increasing the
temperature, stiff particles undergo a first-order solid/liquid transition,
while soft ones undergo a continuous solid/hexatic transition followed by a
discontinuous hexatic/liquid transition. At zero temperature the melting
transition driven by the decrease of the adhesion strength occurs through two
continuous transitions as in the Kosterlitz, Thouless, Halperin, Nelson, and
Young scenario. Thus, there is a range of adhesion strength values where the
hexatic phase is stable at zero temperature, which suggests that the
intermediate phase of the epithelial-to-mesenchymal transition could be hexatic
type.
