Prequel to Defects: Variable Magnitude of Order

This chapter presents an alternative theoretical approach for the xy model, in which the orientational order is characterized by a vector with variable magnitude as well as direction. The free energy can be expressed in terms of this variable-magnitude order parameter, and it can then be minimized to find the core structure of a defect. The theory also predicts the free energy cost of a defect, and the drag force acting on a defect. Based on these results, the chapter compares the unit-vector and variable-magnitude theories, and comments on the general relationship between topology and physics.