Factorization in the multirefined tangent method
When applied to statistical systems showing an arctic curve phenomenon, the tangent method assumes that a modification of the most external path does not affect the arctic curve. We strengthen this statement and also make it more concrete by observing a factorization property: if $Z^{}_{n+k}$ denote...
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Online Access: | http://hdl.handle.net/2078.1/251902 https://doi.org/10.1088/1742-5468/ac1f14 |
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ftunistlouisbrus:oai:dial.uclouvain.be:boreal:251902 2024-05-12T07:59:14+00:00 Factorization in the multirefined tangent method Debin, Bryan Ruelle, Philippe UCL - SST/IRMP - Institut de recherche en mathématique et physique 2021 http://hdl.handle.net/2078.1/251902 https://doi.org/10.1088/1742-5468/ac1f14 eng eng IOP Publishing boreal:251902 http://hdl.handle.net/2078.1/251902 doi:10.1088/1742-5468/ac1f14 urn:EISSN:1742-5468 info:eu-repo/semantics/openAccess Journal of Statistical Mechanics: Theory and Experiment, Vol. 2021, no.10, p. 103201 (2021) Integrable spin chains and vertex models solvable lattice models info:eu-repo/semantics/article 2021 ftunistlouisbrus https://doi.org/10.1088/1742-5468/ac1f14 2024-04-18T17:15:42Z When applied to statistical systems showing an arctic curve phenomenon, the tangent method assumes that a modification of the most external path does not affect the arctic curve. We strengthen this statement and also make it more concrete by observing a factorization property: if $Z^{}_{n+k}$ denotes a refined partition function of a system of $n+k$ non-crossing paths, with the endpoints of the $k$ most external paths possibly displaced, then at dominant order in $n$, it factorizes as $Z^{}_{n+k} \simeq Z^{}_{n} Z_k^{\rm out}$ where $Z_k^{\rm out}$ is the contribution of the $k$ most external paths. Moreover if the shape of the arctic curve is known, we find that the asymptotic value of $Z_k^{\rm out}$ is fully computable in terms of the large deviation function $L$ introduced in \cite{DGR19} (also called Lagrangean function). We present detailed verifications of the factorization in the Aztec diamond and for alternating sign matrices by using exact lattice results. Reversing the argument, we reformulate the tangent method in a way that no longer requires the extension of the domain, and which reveals the hidden role of the $L$ function. As a by-product, the factorization property provides an efficient way to conjecture the asymptotics of multirefined partition functions. Article in Journal/Newspaper Arctic DIAL@USL-B (Université Saint-Louis, Bruxelles) Arctic Journal of Statistical Mechanics: Theory and Experiment 2021 10 103201 |
institution |
Open Polar |
collection |
DIAL@USL-B (Université Saint-Louis, Bruxelles) |
op_collection_id |
ftunistlouisbrus |
language |
English |
topic |
Integrable spin chains and vertex models solvable lattice models |
spellingShingle |
Integrable spin chains and vertex models solvable lattice models Debin, Bryan Ruelle, Philippe Factorization in the multirefined tangent method |
topic_facet |
Integrable spin chains and vertex models solvable lattice models |
description |
When applied to statistical systems showing an arctic curve phenomenon, the tangent method assumes that a modification of the most external path does not affect the arctic curve. We strengthen this statement and also make it more concrete by observing a factorization property: if $Z^{}_{n+k}$ denotes a refined partition function of a system of $n+k$ non-crossing paths, with the endpoints of the $k$ most external paths possibly displaced, then at dominant order in $n$, it factorizes as $Z^{}_{n+k} \simeq Z^{}_{n} Z_k^{\rm out}$ where $Z_k^{\rm out}$ is the contribution of the $k$ most external paths. Moreover if the shape of the arctic curve is known, we find that the asymptotic value of $Z_k^{\rm out}$ is fully computable in terms of the large deviation function $L$ introduced in \cite{DGR19} (also called Lagrangean function). We present detailed verifications of the factorization in the Aztec diamond and for alternating sign matrices by using exact lattice results. Reversing the argument, we reformulate the tangent method in a way that no longer requires the extension of the domain, and which reveals the hidden role of the $L$ function. As a by-product, the factorization property provides an efficient way to conjecture the asymptotics of multirefined partition functions. |
author2 |
UCL - SST/IRMP - Institut de recherche en mathématique et physique |
format |
Article in Journal/Newspaper |
author |
Debin, Bryan Ruelle, Philippe |
author_facet |
Debin, Bryan Ruelle, Philippe |
author_sort |
Debin, Bryan |
title |
Factorization in the multirefined tangent method |
title_short |
Factorization in the multirefined tangent method |
title_full |
Factorization in the multirefined tangent method |
title_fullStr |
Factorization in the multirefined tangent method |
title_full_unstemmed |
Factorization in the multirefined tangent method |
title_sort |
factorization in the multirefined tangent method |
publisher |
IOP Publishing |
publishDate |
2021 |
url |
http://hdl.handle.net/2078.1/251902 https://doi.org/10.1088/1742-5468/ac1f14 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
Journal of Statistical Mechanics: Theory and Experiment, Vol. 2021, no.10, p. 103201 (2021) |
op_relation |
boreal:251902 http://hdl.handle.net/2078.1/251902 doi:10.1088/1742-5468/ac1f14 urn:EISSN:1742-5468 |
op_rights |
info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.1088/1742-5468/ac1f14 |
container_title |
Journal of Statistical Mechanics: Theory and Experiment |
container_volume |
2021 |
container_issue |
10 |
container_start_page |
103201 |
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1798840298287136768 |