In this work, an application of a phase field formulation suitable for modeling the motion of individual partial and full dislocations in hexagonal close packed (HCP) crystals is presented. The formulation incorporates periodic potentials for glide on the distinct HCP slip systems, which are informed here by density functional theory (DFT). The model is applied to simulate the dissociation process starting from an unstable perfect dislocation and ending at its final equilibrium structure for different slip planes and in different HCP metals. The structural characteristics that are predicted for these dislocations include the partial Burgers vectors, dissociation distances, core widths of the partials, and any asymmetries in these quantities. Mg is selected as one of the model materials since its dislocations are the most well studied and it is nearly elastically isotropic. For Mg, it is shown that the predictions for dissociation distances agree with those reported previously by atomic-scale calculations, including density functional theory, for dislocations on the basal < a > , prismatic < a > , and pyramidal type II $<c+a>$ slip systems. Phase field model results are also presented for dislocations in Ti and Zr, which we find develop distinctively different equilibrium structures than Mg.