  Many systems, including biological tissues and foams, are made of highly
packed units having high deformability but low compressibility. At two
dimensions, these systems offer natural tesselations of plane with fixed
density, in which transitions from ordered to disordered patterns are often
observed, in both directions. Using a modified Cellular Potts Model algorithm
that allows rapid thermalization of extensive systems, we numerically explore
the order-disorder transition of monodisperse, two-dimensional cellular systems
driven by thermal agitation. We show that the transition follows most of the
predictions of Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory
developed for melting of 2D solids, extending the validity of this theory to
systems with many-body interactions. In particular, we show the existence of an
intermediate hexatic phase, which preserves the orientational order of the
regular hexagonal tiling, but looses its positional order. In addition to
shedding light on the structural changes observed in experimental systems, our
study shows that soft cellular systems offer macroscopic systems in which KTHNY
melting scenario can be explored, in the continuation of Bragg's experiments on
bubble rafts.
