Grain-boundary theory of melting in two dimensions

A theory of melting in two dimensions via the spontaneous generation of grain boundaries is worked out. We find that this mechanism is more favorable than the dislocation unbinding mechanism and that a first-order phase transition always results. The transition goes from strongly first order to weakly first order for a core energy $E_B$ less than $2.84k{T}_0$ ($T_0$ being the temperature at which the dislocations unbind), consistent with recent estimates by Saito. The question of the hexatic phase is discussed.