A topological defect is a localized obstruction to extending an ordered field smoothly and nonvanishingly through space. Its charge is determined by the homotopy class of the order parameter around the defect.
A domain wall is a codimension-one configuration interpolating between disconnected components of a vacuum manifold. In a one-dimensional system with broken discrete symmetry it is a point defect of finite energy, so positional entropy produces a nonzero density at every positive temperature.
A vortex is a topological defect around which the phase of a complex order parameter has nonzero integer winding. In two dimensions an isolated vortex in a phase-only model has energy proportional to the logarithm of the system size.
Articles by others on the same topic
Topological defects are irregularities or disruptions that occur in a medium where the spatial arrangement of the constituents is defined by a specific order parameter. These defects arise in various fields of physics, particularly in the study of condensed matter systems, cosmology, and field theory. They reflect a mismatch between the local symmetry of the system and the global properties of the medium.