Exponents for Hamiltonian paths on random bicubic maps and KPZ
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 Knizhnik, Polyakov a...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-02-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321323000135 |
| _version_ | 1797897276775989248 |
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| author | Philippe Di Francesco Bertrand Duplantier Olivier Golinelli Emmanuel Guitter |
| author_facet | Philippe Di Francesco Bertrand Duplantier Olivier Golinelli Emmanuel Guitter |
| author_sort | Philippe Di Francesco |
| collection | DOAJ |
| description | 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 Knizhnik, Polyakov and Zamolodchikov (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. |
| first_indexed | 2024-04-10T07:56:03Z |
| format | Article |
| id | doaj.art-16dc649aee8046ddae64a2680515cb8e |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-04-10T07:56:03Z |
| publishDate | 2023-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-16dc649aee8046ddae64a2680515cb8e2023-02-23T04:30:04ZengElsevierNuclear Physics B0550-32132023-02-01987116084Exponents for Hamiltonian paths on random bicubic maps and KPZPhilippe Di Francesco0Bertrand Duplantier1Olivier Golinelli2Emmanuel Guitter3Université Paris-Saclay, CEA, CNRS, Institut de physique théorique, 91191, Gif-sur-Yvette, France; Department of Mathematics, University of Illinois, Urbana, IL 61821, USAUniversité Paris-Saclay, CEA, CNRS, Institut de physique théorique, 91191, Gif-sur-Yvette, FranceUniversité Paris-Saclay, CEA, CNRS, Institut de physique théorique, 91191, Gif-sur-Yvette, FranceUniversité Paris-Saclay, CEA, CNRS, Institut de physique théorique, 91191, Gif-sur-Yvette, France; Corresponding author.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 Knizhnik, Polyakov and Zamolodchikov (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.http://www.sciencedirect.com/science/article/pii/S0550321323000135 |
| spellingShingle | Philippe Di Francesco Bertrand Duplantier Olivier Golinelli Emmanuel Guitter Exponents for Hamiltonian paths on random bicubic maps and KPZ Nuclear Physics B |
| title | Exponents for Hamiltonian paths on random bicubic maps and KPZ |
| title_full | Exponents for Hamiltonian paths on random bicubic maps and KPZ |
| title_fullStr | Exponents for Hamiltonian paths on random bicubic maps and KPZ |
| title_full_unstemmed | Exponents for Hamiltonian paths on random bicubic maps and KPZ |
| title_short | Exponents for Hamiltonian paths on random bicubic maps and KPZ |
| title_sort | exponents for hamiltonian paths on random bicubic maps and kpz |
| url | http://www.sciencedirect.com/science/article/pii/S0550321323000135 |
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