Supercooling-driven glass behaviour in systems exhibiting continuous symmetry breaking

Symmetry breaking is ubiquitous in nature and represents the key mechanism behind rich diversity of patterns exhibited by nature. One commonly introduces an order parameter field to describe onset of qualitatively new ordering in a system on varying a relevant control parameter driving a symmetry breaking transition. In case of continuous symmetry breaking an order parameter consists of two qualitatively different components: an amplitude and gauge field. The latter component enables energy degeneracy and reveals how symmetry is broken. Inherent degeneracy could in general lead to nearby regions exhibiting significantly different gauge fields. Resulting frustrations can nucleate topological defects (TDs) [1]. These represent topologically stable localized nonlinear order parameter solutions. Their key property is a discrete topological charge, which is a conserved quantity. One commonly refers to TDs with positive (negative) charge as defects (antidefects). In general a nearby pair defectantidefect tends to annihilate each order because presence of TDs is in general energetically costly. The total topological charge in a system is conserved for fixed boundary conditions. Consequently number of topological defects could be varied either my merging of relevant TDs or formations of {defect,antidefect} pairs.