Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions
Three-dimensional integer partitions provide a convenient representation of codimension-one three-dimensional random rhombus tilings. Calculating the entropy for such a model is a notoriously difficult problem. We apply transition matrix Monte Carlo simulations to evaluate their entropy with high pr...
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ftunivnantes:oai:HAL:hal-00012894v1 2023-05-15T14:52:15+02:00 Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions Widom, M. Mosseri, R. Destainville, Nicolas Bailly, F. Groupe de Physique des Solides (GPS) Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS) Groupe de Physique Théorique (LPQ) Laboratoire de Physique Quantique (LPQ) Université Toulouse III - Paul Sabatier (UT3) Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3) Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS) Laboratoire de physique des solides et de cristallogénèse (LPSC) Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS) 2002 https://hal.science/hal-00012894 en eng HAL CCSD Springer Verlag info:eu-repo/semantics/altIdentifier/arxiv/cond-mat/0201309 hal-00012894 https://hal.science/hal-00012894 ARXIV: cond-mat/0201309 ISSN: 0022-4715 EISSN: 1572-9613 Journal of Statistical Physics https://hal.science/hal-00012894 Journal of Statistical Physics, 2002, 109, pp.945 [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] info:eu-repo/semantics/article Journal articles 2002 ftunivnantes 2023-02-22T00:32:23Z Three-dimensional integer partitions provide a convenient representation of codimension-one three-dimensional random rhombus tilings. Calculating the entropy for such a model is a notoriously difficult problem. We apply transition matrix Monte Carlo simulations to evaluate their entropy with high precision. We consider both free- and fixed-boundary tilings. Our results suggest that the ratio of free- and fixed-boundary entropies is $\\sigma_{free}/\\sigma_{fixed}=3/2$, and can be interpreted as the ratio of the volumes of two simple, nested, polyhedra. This finding supports a conjecture by Linde, Moore and Nordahl concerning the ''arctic octahedron phenomenon\'\' in three-dimensional random tilings. Article in Journal/Newspaper Arctic Université de Nantes: HAL-UNIV-NANTES Arctic Linde ENVELOPE(124.611,124.611,64.968,64.968) |
institution |
Open Polar |
collection |
Université de Nantes: HAL-UNIV-NANTES |
op_collection_id |
ftunivnantes |
language |
English |
topic |
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] |
spellingShingle |
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] Widom, M. Mosseri, R. Destainville, Nicolas Bailly, F. Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions |
topic_facet |
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] |
description |
Three-dimensional integer partitions provide a convenient representation of codimension-one three-dimensional random rhombus tilings. Calculating the entropy for such a model is a notoriously difficult problem. We apply transition matrix Monte Carlo simulations to evaluate their entropy with high precision. We consider both free- and fixed-boundary tilings. Our results suggest that the ratio of free- and fixed-boundary entropies is $\\sigma_{free}/\\sigma_{fixed}=3/2$, and can be interpreted as the ratio of the volumes of two simple, nested, polyhedra. This finding supports a conjecture by Linde, Moore and Nordahl concerning the ''arctic octahedron phenomenon\'\' in three-dimensional random tilings. |
author2 |
Groupe de Physique des Solides (GPS) Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS) Groupe de Physique Théorique (LPQ) Laboratoire de Physique Quantique (LPQ) Université Toulouse III - Paul Sabatier (UT3) Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3) Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS) Laboratoire de physique des solides et de cristallogénèse (LPSC) Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS) |
format |
Article in Journal/Newspaper |
author |
Widom, M. Mosseri, R. Destainville, Nicolas Bailly, F. |
author_facet |
Widom, M. Mosseri, R. Destainville, Nicolas Bailly, F. |
author_sort |
Widom, M. |
title |
Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions |
title_short |
Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions |
title_full |
Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions |
title_fullStr |
Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions |
title_full_unstemmed |
Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions |
title_sort |
arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions |
publisher |
HAL CCSD |
publishDate |
2002 |
url |
https://hal.science/hal-00012894 |
long_lat |
ENVELOPE(124.611,124.611,64.968,64.968) |
geographic |
Arctic Linde |
geographic_facet |
Arctic Linde |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
ISSN: 0022-4715 EISSN: 1572-9613 Journal of Statistical Physics https://hal.science/hal-00012894 Journal of Statistical Physics, 2002, 109, pp.945 |
op_relation |
info:eu-repo/semantics/altIdentifier/arxiv/cond-mat/0201309 hal-00012894 https://hal.science/hal-00012894 ARXIV: cond-mat/0201309 |
_version_ |
1766323474737922048 |