Research on the coherent distribution of order parameters determining phase existence regions in the two-component Ginzburg-Landau model is reviewed. A major result of this research, obtained by formulating this model in terms of gauged order parameters (the unit vector field n, the density ρ², and the particle momentum c), is that some of the universal phase and field configuration properties are determined by topological features related to the Hopf invariant Q and its generalizations. For sufficiently low densities, a ring-shaped density distribution may be favored over stripes. For an L < Q phase (L being the mutual linking index of the n and c field configurations), a gain in free energy occurs when a transition to a nonuniform current state occurs. A universal mechanism accounting for decorrelation with increasing charge density is discussed. The second part of the review is concerned with implications of non-Abelian field theory for knotted configurations. The key properties of semiclassical configurations arising in the Yang-Mills theory and the Skyrme model are discussed in detail, and the relation of these configurations to knotted distributions is scrutinized.

PACS: 02.40.−k, 11.15.−q, 11.27.+d, 74.20.De (all) DOI: 10.1070/PU2006v049n07ABEH006022 URL: https://ufn.ru/en/articles/2006/7/a/ 000242169200001 2-s2.0-33751345507 2006PhyU...49..667P Citation: Protogenov A P "Knots and links in the order parameter distributions of strongly correlated systems" Phys. Usp. 49 667–691 (2006) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Протогенов А П «Узлы и зацепления распределений параметров порядка в сильно коррелированных системах» УФН 176 689–715 (2006); DOI: 10.3367/UFNr.0176.200607a.0689