Dual model for dislocation and disclination melting

We show that defect melting involving dislocations and disclinations is dually equivalent to an extension of an XY model with an energy of the type Σ_{i, j}{cos(?_iu_j + ?_ju_i) + ? cos ?_iω_j] }, where $\text{ω}{}_{\mathrm{t}}\text{=}\text{1}\text{2}\text{?}{}_{\mathrm{tjk}}\text{?}{}_{\mathrm{j}}\text{u}{}_{\mathrm{k}}$ is the local rotation field. The. model clarifies the proper choice of defect core energies arising from nonlinear elasticity. These permit the pile-up of dislocations to disclinations which is essential for the first order of the melting transition.