We classify the sectors of configurations that result from the dynamics of 2d crossing flux lines, which are the simplest degrees of freedom of the 3-coloring lattice model. We show that the dynamical obstruction is the consequence of two effects: (i) conservation laws described by a set of invariants that are polynomials of the winding numbers of the loop configuration, (ii) steric obstruction that prevents paths between configurations, for lack of free space. We argue that the invariants fully classify the configurations in five, chiral and achiral, sectors and no further obstruction in the limit of low-winding numbers.
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- 1 Olivier CEPAS,
- 2 3 Peter M. Akhmetiev
- 1 Universite Grenoblé Alpes / Grenoble Alpes University [UGA]
- 2 Институт земного магнетизма, ионосферы и распространения радиоволн им. Н. В. Пушкова / Institute of Terrestrial Magnetism Ionosphere and Radio Wave Propagation [IZMIRAN]
- 3 Высшая школа экономики / National Research University Higher School of Economics [HSE]