We examine the fluid-solid transition for a hard-disk system. By counting the near neighbors in the average configurations of a grand-canonical Monte Carlo simulation, this enables us to relate the thermodynamic transition with the rigidity theory, since we find that the coordination number in the fluid-solid transition is close to the coordination number predicted by a mean field rigidity theory, due to dynamical jamming of particles, where the contact region between disks is the radial ring outside a disk with a maximum allowed coordination number that is not bigger than six. Using these ideas, we were able to produce a continuous glass-like transition when nucleation of rigidity is suppressed.
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