Colorings of odd or even chirality on hexagonal lattices

Abstract

We define two classes of colorings that have odd or even chirality on hexagonal lattices. This parity is an invariant in the dynamics of all loops, and explains why standard Monte-Carlo algorithms are nonergodic. We argue that adding the motion of "stranded" loops allows for parity changes. By implementing this algorithm, we show that the even and odd classes have the same entropy. In general, they do not have the same number of states, except for the special geometry of long strips, where a Z${}_2$ symmetry between even and odd states occurs in the thermodynamic limit.

arXiv comment18 pages, 13 figures

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Cited by in corpus (6)

• Quantum versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho3Mg2Sb3O14
• Probing many-body localization in a disordered quantum dimer model on the honeycomb lattice
• Color-dependent interactions in the three coloring model
• Hamiltonian cycles and 1-factors in 5-regular graphs
• Invariants of winding-numbers and steric obstruction in dynamics of flux lines
• Phase-space networks and connectivity of the kagome antiferromagnet