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Invariants of winding-numbers and steric obstruction in dynamics of flux lines

Olivier Cépas, Peter M. Akhmetiev

SciPost Phys. 7, 032 (2019) · published 12 September 2019


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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Flux lines Winding numbers

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