Elastic moduli, dislocation core energy, and melting of hard disks in two dimensions

Elastic moduli and dislocation core energy of the triangular solid of hard disks of diameter sigma are obtained in the limit of vanishing dislocation-antidislocation pair density, from Monte Carlo simulations that incorporate a constraint, namely that all moves altering the local connectivity away from that of the ideal triangular lattice are rejected. In this limit we show that the solid is stable against all other fluctuations at least up to densities as low as rhosigma(2)=0.88. Our system does not show any phase transition so diverging correlation lengths leading to finite size effects and slow relaxations do not exist. The dislocation pair formation probability is estimated from the fraction of moves rejected due to the constraint which yields, in turn, the core energy E(c) and the (bare) dislocation fugacity y. Using these quantities, we check the relative validity of first order and Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) melting scenarios and obtain numerical estimates of the typical expected transition densities and pressures. We conclude that a KTHNY transition from the solid to a hexatic phase preempts the solid to liquid first order transition in this system albeit by a very small margin, easily masked by crossover effects in unconstrained "brute- force" simulations with a small number of particles.