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Article Dans Une Revue Nuclear Physics B Année : 2023

Exponents for Hamiltonian paths on random bicubic maps and KPZ

Résumé

We evaluate the configuration exponents of various ensembles of Hamiltonian paths drawn on random planar bicubic maps. These exponents are estimated from the extrapolations of exact enumeration results for finite sizes and compared with their theoretical predictions based on the KPZ relations, as applied to their regular counterpart on the honeycomb lattice. We show that a naive use of these relations does not reproduce the measured exponents but that a simple modification in their application may possibly correct the observed discrepancy. We show that a similar modification is required to reproduce via the KPZ formulas some exactly known exponents for the problem of unweighted fully packed loops on random planar bicubic maps.

Dates et versions

hal-03821510 , version 1 (19-10-2022)

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Philippe Di Francesco, Bertrand Duplantier, Olivier Golinelli, Emmanuel Guitter. Exponents for Hamiltonian paths on random bicubic maps and KPZ. Nuclear Physics B, 2023, 987, pp.116084. ⟨10.1016/j.nuclphysb.2023.116084⟩. ⟨hal-03821510⟩
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