Algebraic area enumeration of random walks on the honeycomb lattice – Archive ouverte HAL

Li Gan ¹ Stéphane Ouvry ¹ Alexios P. Polychronakos

Li Gan, Stéphane Ouvry, Alexios P. Polychronakos. Algebraic area enumeration of random walks on the honeycomb lattice. Phys.Rev.E, 2022, 105 (1), pp.014112. ⟨10.1103/PhysRevE.105.014112⟩. ⟨hal-03318233⟩

We study the enumeration of closed walks of given length and algebraic area on the honeycomb lattice. Using an irreducible operator realization of honeycomb lattice moves, we map the problem to a Hofstadter-like Hamiltonian and show that the generating function of closed walks maps to the grand partition function of a system of particles with exclusion statistics of order

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