Fig. 1: Schematic representation of 3D point defects.
a Discrete vector at a simple cubic lattice corner illustrating a radially outward field for a monopole with Q = +1 (red). A vertex x* is shown where \({\overrightarrow{s}}_{1}\), \({\overrightarrow{s}}_{2}\), \({\overrightarrow{s}}_{3}\) and \({\overrightarrow{s}}_{4}\) field is at the four corners of the vertex. b Continuous vector field (left) and discrete vector field (right) for a monopole. c Radially inward field representing an anti-monopole with Q = −1 (blue). d Continuous (left) and discrete (right) vector fields for Q = −1. e Radial defects with Q = ±1 are shown along with the 2D winding numbers of the projected vectors onto the faces of a cube. Negative 2D winding number (q2D = −1) is indicated in orange, positive (q2D = +1) in green. Stars mark the locations of the 2D point defects, while the corresponding surfaces are colored according to their winding number. f Hyperbolic defects with Q = ±1 are displayed with projected vectors and their associated winding numbers, using the same color scheme as in (e).
