Calculation of partition functions by measuring component distributions

A new algorithm is presented, which allows us to calculate numerically the partition function Z for systems, which can be described by arbitrary interaction graphs and lattices, e.g., Ising models or Potts models (for arbitrary values q>0), including random or diluted models. The new approach is...

Full description

Saved in:
Bibliographic Details
Published in:Physical review letters 2005-02, Vol.94 (5), p.050601.1-050601.4, Article 050601
Main Author: HARTMANN, A. K
Format: Article
Language:English
Subjects:
Exact sciences and technology
Physics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c337t-1980180c7678b078a8a40233ae03e967e97c06318f5219e50417dbd7d3c118813
cites cdi_FETCH-LOGICAL-c337t-1980180c7678b078a8a40233ae03e967e97c06318f5219e50417dbd7d3c118813
container_end_page 050601.4
container_issue 5
container_start_page 050601.1
container_title Physical review letters
container_volume 94
creator HARTMANN, A. K
description A new algorithm is presented, which allows us to calculate numerically the partition function Z for systems, which can be described by arbitrary interaction graphs and lattices, e.g., Ising models or Potts models (for arbitrary values q>0), including random or diluted models. The new approach is suitable for large systems. The basic idea is to measure the distribution of the number of connected components in the corresponding Fortuin-Kasteleyn representation and to compare with the case of zero degrees of freedom, where the exact result Z=1 is known. As an application, d=2 and d=3 dimensional ferromagnetic Potts models are studied, and the critical values qc, where the transition changes from second to first order, are determined. Large systems of sizes N=1000(2) and N=100(3) are treated. The critical value qc(d=2)=4 is confirmed and qc(d=3)=2.35(5) is found.
doi_str_mv 10.1103/PhysRevLett.94.050601
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_67542929</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>67542929</sourcerecordid><originalsourceid>FETCH-LOGICAL-c337t-1980180c7678b078a8a40233ae03e967e97c06318f5219e50417dbd7d3c118813</originalsourceid><addsrcrecordid>eNpNkE1LxDAQhoMo7rr6E5Re9NZ1Jmmb5CiLrsKCInoOaZpqpV8mqbD_3u5uQU_zDjzvDDyEXCIsEYHdvnxu_av92dgQljJZQgoZ4BGZI3AZc8TkmMwBGMYSgM_ImfdfAIA0E6dkhikXLKN0TtYrXZuh1qHq2qgro167UO2XcmjNLvgo30aN1X5wVfsRma7pu9a2ISoqH1yVD3vonJyUuvb2YpoL8v5w_7Z6jDfP66fV3SY2jPEQoxSAAgzPuMiBCy10ApQxbYFZmXEruYGMoShTitKmkCAv8oIXzCAKgWxBbg53e9d9D9YH1VTe2LrWre0GrzKeJlRSOYLpATSu897ZUvWuarTbKgS1M6j-GVQyUQeDY-9qejDkjS3-WpOyEbieAO2NrkunW1P5Py4bwZQC-wWVK3xB</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>67542929</pqid></control><display><type>article</type><title>Calculation of partition functions by measuring component distributions</title><source>American Physical Society:Jisc Collections:APS Read and Publish 2023-2025 (reading list)</source><creator>HARTMANN, A. K</creator><creatorcontrib>HARTMANN, A. K</creatorcontrib><description>A new algorithm is presented, which allows us to calculate numerically the partition function Z for systems, which can be described by arbitrary interaction graphs and lattices, e.g., Ising models or Potts models (for arbitrary values q&gt;0), including random or diluted models. The new approach is suitable for large systems. The basic idea is to measure the distribution of the number of connected components in the corresponding Fortuin-Kasteleyn representation and to compare with the case of zero degrees of freedom, where the exact result Z=1 is known. As an application, d=2 and d=3 dimensional ferromagnetic Potts models are studied, and the critical values qc, where the transition changes from second to first order, are determined. Large systems of sizes N=1000(2) and N=100(3) are treated. The critical value qc(d=2)=4 is confirmed and qc(d=3)=2.35(5) is found.</description><identifier>ISSN: 0031-9007</identifier><identifier>EISSN: 1079-7114</identifier><identifier>DOI: 10.1103/PhysRevLett.94.050601</identifier><identifier>PMID: 15783622</identifier><identifier>CODEN: PRLTAO</identifier><language>eng</language><publisher>Ridge, NY: American Physical Society</publisher><subject>Exact sciences and technology ; Physics</subject><ispartof>Physical review letters, 2005-02, Vol.94 (5), p.050601.1-050601.4, Article 050601</ispartof><rights>2005 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c337t-1980180c7678b078a8a40233ae03e967e97c06318f5219e50417dbd7d3c118813</citedby><cites>FETCH-LOGICAL-c337t-1980180c7678b078a8a40233ae03e967e97c06318f5219e50417dbd7d3c118813</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=16578520$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/15783622$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>HARTMANN, A. K</creatorcontrib><title>Calculation of partition functions by measuring component distributions</title><title>Physical review letters</title><addtitle>Phys Rev Lett</addtitle><description>A new algorithm is presented, which allows us to calculate numerically the partition function Z for systems, which can be described by arbitrary interaction graphs and lattices, e.g., Ising models or Potts models (for arbitrary values q&gt;0), including random or diluted models. The new approach is suitable for large systems. The basic idea is to measure the distribution of the number of connected components in the corresponding Fortuin-Kasteleyn representation and to compare with the case of zero degrees of freedom, where the exact result Z=1 is known. As an application, d=2 and d=3 dimensional ferromagnetic Potts models are studied, and the critical values qc, where the transition changes from second to first order, are determined. Large systems of sizes N=1000(2) and N=100(3) are treated. The critical value qc(d=2)=4 is confirmed and qc(d=3)=2.35(5) is found.</description><subject>Exact sciences and technology</subject><subject>Physics</subject><issn>0031-9007</issn><issn>1079-7114</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><recordid>eNpNkE1LxDAQhoMo7rr6E5Re9NZ1Jmmb5CiLrsKCInoOaZpqpV8mqbD_3u5uQU_zDjzvDDyEXCIsEYHdvnxu_av92dgQljJZQgoZ4BGZI3AZc8TkmMwBGMYSgM_ImfdfAIA0E6dkhikXLKN0TtYrXZuh1qHq2qgro167UO2XcmjNLvgo30aN1X5wVfsRma7pu9a2ISoqH1yVD3vonJyUuvb2YpoL8v5w_7Z6jDfP66fV3SY2jPEQoxSAAgzPuMiBCy10ApQxbYFZmXEruYGMoShTitKmkCAv8oIXzCAKgWxBbg53e9d9D9YH1VTe2LrWre0GrzKeJlRSOYLpATSu897ZUvWuarTbKgS1M6j-GVQyUQeDY-9qejDkjS3-WpOyEbieAO2NrkunW1P5Py4bwZQC-wWVK3xB</recordid><startdate>20050211</startdate><enddate>20050211</enddate><creator>HARTMANN, A. K</creator><general>American Physical Society</general><scope>IQODW</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope></search><sort><creationdate>20050211</creationdate><title>Calculation of partition functions by measuring component distributions</title><author>HARTMANN, A. K</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c337t-1980180c7678b078a8a40233ae03e967e97c06318f5219e50417dbd7d3c118813</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Exact sciences and technology</topic><topic>Physics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>HARTMANN, A. K</creatorcontrib><collection>Pascal-Francis</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><jtitle>Physical review letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>HARTMANN, A. K</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Calculation of partition functions by measuring component distributions</atitle><jtitle>Physical review letters</jtitle><addtitle>Phys Rev Lett</addtitle><date>2005-02-11</date><risdate>2005</risdate><volume>94</volume><issue>5</issue><spage>050601.1</spage><epage>050601.4</epage><pages>050601.1-050601.4</pages><artnum>050601</artnum><issn>0031-9007</issn><eissn>1079-7114</eissn><coden>PRLTAO</coden><abstract>A new algorithm is presented, which allows us to calculate numerically the partition function Z for systems, which can be described by arbitrary interaction graphs and lattices, e.g., Ising models or Potts models (for arbitrary values q&gt;0), including random or diluted models. The new approach is suitable for large systems. The basic idea is to measure the distribution of the number of connected components in the corresponding Fortuin-Kasteleyn representation and to compare with the case of zero degrees of freedom, where the exact result Z=1 is known. As an application, d=2 and d=3 dimensional ferromagnetic Potts models are studied, and the critical values qc, where the transition changes from second to first order, are determined. Large systems of sizes N=1000(2) and N=100(3) are treated. The critical value qc(d=2)=4 is confirmed and qc(d=3)=2.35(5) is found.</abstract><cop>Ridge, NY</cop><pub>American Physical Society</pub><pmid>15783622</pmid><doi>10.1103/PhysRevLett.94.050601</doi><tpages>1</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0031-9007
ispartof Physical review letters, 2005-02, Vol.94 (5), p.050601.1-050601.4, Article 050601
issn 0031-9007
1079-7114
language eng
recordid cdi_proquest_miscellaneous_67542929
source American Physical Society:Jisc Collections:APS Read and Publish 2023-2025 (reading list)
subjects Exact sciences and technology
Physics
title Calculation of partition functions by measuring component distributions
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T21%3A20%3A36IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Calculation%20of%20partition%20functions%20by%20measuring%20component%20distributions&rft.jtitle=Physical%20review%20letters&rft.au=HARTMANN,%20A.%20K&rft.date=2005-02-11&rft.volume=94&rft.issue=5&rft.spage=050601.1&rft.epage=050601.4&rft.pages=050601.1-050601.4&rft.artnum=050601&rft.issn=0031-9007&rft.eissn=1079-7114&rft.coden=PRLTAO&rft_id=info:doi/10.1103/PhysRevLett.94.050601&rft_dat=%3Cproquest_cross%3E67542929%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c337t-1980180c7678b078a8a40233ae03e967e97c06318f5219e50417dbd7d3c118813%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=67542929&rft_id=info:pmid/15783622&rfr_iscdi=true