Marshall Rosenbluth and the Metropolis algorithma) | Physics of Plasmas

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Plasmas" /><meta name="citation_volume" content="12" /><meta name="citation_issue" content="5" /><meta name="citation_publication_date" content="2005/05/01" /><meta name="citation_issn" content="1070-664X" /><meta name="citation_publisher" content="AIP Publishing" /><meta name="citation_reference" content="citation_author=Metropolis N.; citation_author=Rosenbluth A. W.; citation_author=Rosenbluth M. N.; citation_author=Teller A. H.; citation_author=Teller E.; citation_journal_title=J. Chem. Phys.; citation_year=1953; citation_volume=21; citation_pages=1087" /><meta name="citation_reference" content="citation_author=Rosenbluth M. N.; citation_author=Gubernatis J. E.; citation_publisher=American Institute of Physics, ; citation_title=The Monte Carlo Method in the Physical Sciences; citation_year=2003; citation_pages=22" /><meta name="citation_reference" content="citation_author=Gubernatis J. E.; citation_author=Gubernatis J. E.; citation_publisher=American Institute of Physics, ; citation_title=The Monte Carlo Method in the Physical Sciences; citation_year=2003; citation_pages=3" /><meta name="citation_reference" content="Rosenbluth A. W. (private communication). " /><meta name="citation_reference" content="citation_author=Alder B. J.; citation_author=Wainwright T. E.; citation_journal_title=J. Chem. Phys.; citation_year=1957; citation_volume=27; citation_pages=1208" /><meta name="citation_reference" content="citation_author=Wood W. W.; citation_author=Jacobson J. D.; citation_journal_title=J. Chem. Phys.; citation_year=1957; citation_volume=27; citation_pages=1207" /><meta name="citation_reference" content="citation_author=Wood W. W.; citation_author=Gubernatis J. E.; citation_publisher=American Institute of Physics, ; citation_title=The Monte Carlo Method in the Physical Sciences; citation_year=2003; citation_pages=39" /><meta name="citation_reference" content="citation_author=Meyer H. A.; citation_publisher=Wiley, ; citation_title=Symposium on Monte Carlo Methods; citation_year=1956; " /><meta name="citation_reference" content="citation_author=Rosenbluth M. N.; citation_author=Gubernatis J. E.; citation_publisher=American Institute of Physics, ; citation_title=The Monte Carlo Method in the Physical Sciences; citation_year=2003; citation_pages=32" /><meta name="citation_reference" content="citation_author=Gupta R.; citation_author=Gubernatis J. E.; citation_publisher=American Institute of Physics, ; citation_title=The Monte Carlo Method in the Physical Sciences; citation_year=2003; citation_pages=110" /><meta name="citation_pdf_url" content="https://pubs.aip.org/aip/pop/article-pdf/doi/10.1063/1.1887186/13509783/057303_1_online.pdf" /><meta name="dc.identifier" content="10.1063/1.1887186" /><meta name="description" content="The 1953 publication, “Equation of State Calculations by Very Fast Computing Machines” by N. Metropolis, A. W. Rosenbluth and M. N. Rosenbluth, and M. Teller an" /><meta property="og:updated_time" content="4/28/2005" /> <meta property="og:type" content="article" /> <meta property="og:title" content="Marshall Rosenbluth and the Metropolis algorithm" /> <meta property="og:description" content="The 1953 publication, “Equation of State Calculations by Very Fast Computing Machines” by N. Metropolis, A. W. Rosenbluth and M. N. Rosenbluth, and M. Teller an" /> <meta property="og:url" content="/aip/pop/article/12/5/057303/1016565/Marshall-Rosenbluth-and-the-Metropolis-algorithma" /> <meta property="og:site_name" content="AIP Publishing" /> <meta property="og:image" content="https://aipp.silverchair-cdn.com/aipp/content_public/journal/pop/12/5/10.1063_1.1887186/1/057303_1_f1.jpeg?Expires=1735416456&Signature=UB0mjIwMhxqOeOS1Sri3-o0R3zcMKnSvGkTv-ktqclV2v58SsIMHQidBkEVdSkxc0PyVBnT~enlx1uwdNtLOOMTQwu4roTKq8tTLEuSAVIEBjcUpViQWlvFXUFP1w8J0Eg3cihSR3oWq9KoxJonio3yIU6q-xHltFvbm1XlacA-fJAVrGC9cNRl97ukhEVIA9V-H~KyY3yM5c~6sl7jYRmJE6vqGfEi1DJwU6FEnerDHvp30wdsEFJtq5cHgeGFiCo-Xai~kuTTEabT0U67tSC7uyQiKsbXdjeh7fEb03RSKxxcUHQUSyP~kAabNA5vKQQDlG0iDgZ3lVcSGouipRg__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA" /> <meta property="og:image:url" content="https://aipp.silverchair-cdn.com/aipp/content_public/journal/pop/12/5/10.1063_1.1887186/1/057303_1_f1.jpeg?Expires=1735416456&Signature=UB0mjIwMhxqOeOS1Sri3-o0R3zcMKnSvGkTv-ktqclV2v58SsIMHQidBkEVdSkxc0PyVBnT~enlx1uwdNtLOOMTQwu4roTKq8tTLEuSAVIEBjcUpViQWlvFXUFP1w8J0Eg3cihSR3oWq9KoxJonio3yIU6q-xHltFvbm1XlacA-fJAVrGC9cNRl97ukhEVIA9V-H~KyY3yM5c~6sl7jYRmJE6vqGfEi1DJwU6FEnerDHvp30wdsEFJtq5cHgeGFiCo-Xai~kuTTEabT0U67tSC7uyQiKsbXdjeh7fEb03RSKxxcUHQUSyP~kAabNA5vKQQDlG0iDgZ3lVcSGouipRg__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA" /> <meta property="og:image:alt" content="FIG. 1. Monte Carlo simulation of a system of hard disks. Each Monte Carlo step consists of proposing a move of one disk, repositioning its center to some random position inside a small square. If the move is accepted or rejected via the Metropolis algorithm, such movements will eventually sample the Boltzmann distribution. Instead of a square, a circle, for instance, could be also used. The efficiency of the simulation is controlled by the size of this square or circle." /> <meta name="citation_xml_url" content="https://pubs.aip.org/aip/pop/article-xml/doi/10.1063/1.1887186/1016565" /> <meta name="description" content="The 1953 publication, “Equation of State Calculations by Very Fast Computing Machines” by N. Metropolis, A. W. Rosenbluth and M. N. Rosenbluth, and M. 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Am. Phys. Soc. <strong>49</strong>, 173 (2004).</p></div> </div> </div> </div> </div> <div class="pub-history-wrap clearfix"> <div class="pub-history-row clearfix"> <div class="ww-citation-primary"><em>Phys. Plasmas</em> 12, 057303 (2005)</div> </div> <div class="pub-history-row citation-wrap-row clearfix"> <div class="ww-citation-wrap-doi"> <div class="citation-doi"> <a href="https://doi.org/10.1063/1.1887186">https://doi.org/10.1063/1.1887186</a> </div> </div> <div class="ww-citation-history-wrap js-history-dropdown-wrap"> <a href="javascript:;" class="history-label js-history-dropdown-trigger"> <span>Article history</span><i class="icon-history-small"></i> </a> <div class="ww-history js-history-entries-wrap"> <div class="history-entry"> <div class="wi-state">Received:</div> <div class="wi-date">November 29 2004</div> </div> <div class="history-entry"> <div class="wi-state">Accepted:</div> <div class="wi-date">February 14 2005</div> </div> </div> </div> </div> </div> </div> </div> <script> $(document).ready(function () { $('.article-top-widget').on('click', '.ati-toggle-trigger', function () { $(this).find('.icon-general-add, .icon-minus').toggleClass('icon-minus icon-general-add'); 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class="widget-items" data-widgetname="ArticleFulltext"> <div id="62945215" class="article-section-wrapper js-article-section js-content-section " data-section-parent-id="0"> <section class="abstract"><p class="citation-paragraph">The 1953 publication, “Equation of State Calculations by Very Fast Computing Machines” by N. Metropolis, A. W. Rosenbluth and M. N. Rosenbluth, and M. Teller and E. Teller<span class="citation mixed-citation"> [<span class="source">J. Chem. Phys.</span> <span class="volume">21</span>, <span class="fpage">1087</span> (<span class="year">1953</span>)</span>] marked the beginning of the use of the Monte Carlo method for solving problems in the physical sciences. The method described in this publication subsequently became known as the Metropolis algorithm, undoubtedly the most famous and most widely used Monte Carlo algorithm ever published. As none of the authors made subsequent use of the algorithm, they became unknown to the large simulation physics community that grew from this publication and their roles in its development became the subject of mystery and legend. At a conference marking the 50th anniversary of the 1953 publication, Marshall Rosenbluth gave his recollections of the algorithm’s development. The present paper describes the algorithm, reconstructs the historical context in which it was developed, and summarizes Marshall’s recollections.</p></section> </div> <div class="article-metadata-panel clearfix rs_skip"> <div class="widget-SolrResourceMetadata widget-instance-ContentMetadata_ArticleFulltext_Article"> <div class="content-metadata-taxonomies"> <div class="content-metadata"> <div class="content-metadata-taxonomies-title">Topics</div> <a href="/pop/search-results?page=1&tax=P1698P43035">Atomic energy</a><span>,</span> <a href="/pop/search-results?page=1&tax=P2163P1736">Equations of state</a><span>,</span> <a href="/pop/search-results?page=1&tax=P3437P48621">Numerical integration</a><span>,</span> <a href="/pop/search-results?page=1&tax=P4055P4074">Nuclear weapons</a><span>,</span> <a href="/pop/search-results?page=1&tax=P4547C6973">Chemical elements</a><span>,</span> <a href="/pop/search-results?page=1&tax=P4675P4675">Plasma physics</a><span>,</span> <a href="/pop/search-results?page=1&tax=P5789C1045">Statistical mechanics</a><span>,</span> <a href="/pop/search-results?page=1&tax=P5789C1347">Statistical thermodynamics</a><span>,</span> <a href="/pop/search-results?page=1&tax=P5789P3398">Markov processes</a><span>,</span> <a href="/pop/search-results?page=1&tax=P5789P3731">Monte Carlo methods</a> </div> </div> </div> </div> <h2 scrollto-destination="62945267" id="62945267" data-section-title="REFERENCES" class="backreferences-title jumplink-heading">REFERENCES</h2> <div class=""> <div id="62945267" class="article-section-wrapper js-article-section js-content-section " data-section-parent-id="0"> <div class="ref-list js-splitview-ref-list"><div data-content-id="c1" xmlns:helper="urn:XsltStringHelper"><div class="ref false"><div class="ref-content "><span class="label title-label">1.</span><div class="citation mixed-citation"><span class="name string-name"><div class="given-names">N.</div> <div class="surname">Metropolis</div></span>, <span class="name string-name"><div class="given-names">A. W.</div> <div class="surname">Rosenbluth</div></span>, <span class="name string-name"><div class="given-names">M. N.</div> <div class="surname">Rosenbluth</div></span>, <span class="name string-name"><div class="given-names">A. H.</div> <div class="surname">Teller</div></span>, and <span class="name string-name"><div class="given-names">E.</div> <div class="surname">Teller</div></span>, <div class="source">J. Chem. Phys.</div><div class="pub-id-doi"><a href="https://doi.org/10.1063/1.1699114" class="link link-pub-id-doi openInAnotherWindow" target="_blank"> https://doi.org/10.1063/1.1699114</a></div> <div class="volume">21</div>, <div class="fpage">1087</div> (<div class="year">1953</div>).<div class="citation-links"><div class="google-scholar-ref-link js-ref-link"><a href="https://scholar.google.com/scholar_lookup?title=&author=N.%20Metropolis&author=A.%20W.%20Rosenbluth&author=M.%20N.%20Rosenbluth&author=A.%20H.%20Teller&author=E.%20Teller&publication_year=1953&journal=J.%20Chem.%20Phys.&volume=21&pages=1087" target="_blank">Google Scholar</a></div><div class="crossref-doi js-ref-link"><a class="openInAnotherWindow" href="http://dx.doi.org/10.1063/1.1699114" target="_blank">Crossref</a></div><div class="adsDoiReference hide"><a class="openInAnotherWindow" href="http://adsabs.harvard.edu/cgi-bin/basic_connect?qsearch=10.1063%2F1.1699114" target="_blank">Search ADS</a></div><div class="xslopenurl empty-target"><span class="inst-open-url-holders" data-targetId="10.1063%2F1.1699114"> </span></div> </div></div></div></div></div><div data-content-id="c2" xmlns:helper="urn:XsltStringHelper"><div class="ref false"><div class="ref-content "><span class="label title-label">2.</span><div class="citation mixed-citation"><span class="name string-name"><div class="given-names">M. N.</div> <div class="surname">Rosenbluth</div></span>, in <div class="source">The Monte Carlo Method in the Physical Sciences</div>, edited by <span class="person-group"><span class="name string-name"><div class="given-names">J. E.</div> <div class="surname">Gubernatis</div></span></span> (<div class="publisher-name">American Institute of Physics</div>, New York, <div class="year">2003</div>), p. <div class="fpage">22</div>.<div class="citation-links"><div class="google-scholar-ref-link js-ref-link"><a href="https://scholar.google.com/scholar_lookup?title=The%20Monte%20Carlo%20Method%20in%20the%20Physical%20Sciences&author=M.%20N.%20Rosenbluth&author=J.%20E.%20Gubernatis&publication_year=2003&book=The%20Monte%20Carlo%20Method%20in%20the%20Physical%20Sciences" target="_blank">Google Scholar</a></div> </div></div></div></div></div><div data-content-id="c3" xmlns:helper="urn:XsltStringHelper"><div class="ref false"><div class="ref-content "><span class="label title-label">3.</span><div class="citation mixed-citation">Some pre- and post-history to the algorithm are discussed by <span class="name string-name"><div class="given-names">J. E.</div> <div class="surname">Gubernatis</div></span>, in <div class="source">The Monte Carlo Method in the Physical Sciences</div>, edited by <span class="person-group"><span class="name string-name"><div class="given-names">J. E.</div> <div class="surname">Gubernatis</div></span></span> (<div class="publisher-name">American Institute of Physics</div>, New York, <div class="year">2003</div>), p. <div class="fpage">3</div>.<div class="citation-links"><div class="google-scholar-ref-link js-ref-link"><a href="https://scholar.google.com/scholar_lookup?title=The%20Monte%20Carlo%20Method%20in%20the%20Physical%20Sciences&author=J.%20E.%20Gubernatis&author=J.%20E.%20Gubernatis&publication_year=2003&book=The%20Monte%20Carlo%20Method%20in%20the%20Physical%20Sciences" target="_blank">Google Scholar</a></div> </div></div></div></div></div><div data-content-id="c4" xmlns:helper="urn:XsltStringHelper"><div class="ref false"><div class="ref-content "><span class="label title-label">4.</span><div class="citation mixed-citation"><span class="name string-name"><div class="given-names">A. W.</div> <div class="surname">Rosenbluth</div></span> (private communication).</div></div></div></div><div data-content-id="c5" xmlns:helper="urn:XsltStringHelper"><div class="ref false"><div class="ref-content "><span class="label title-label">5.</span><div class="citation mixed-citation"><span class="name string-name"><div class="given-names">B. J.</div> <div class="surname">Alder</div></span> and <span class="name string-name"><div class="given-names">T. E.</div> <div class="surname">Wainwright</div></span>, <div class="source">J. Chem. Phys.</div><div class="pub-id-doi"><a href="https://doi.org/10.1063/1.1743957" class="link link-pub-id-doi openInAnotherWindow" target="_blank"> https://doi.org/10.1063/1.1743957</a></div> <div class="volume">27</div>, <div class="fpage">1208</div> (<div class="year">1957</div>).<div class="citation-links"><div class="google-scholar-ref-link js-ref-link"><a href="https://scholar.google.com/scholar_lookup?title=&author=B.%20J.%20Alder&author=T.%20E.%20Wainwright&publication_year=1957&journal=J.%20Chem.%20Phys.&volume=27&pages=1208" target="_blank">Google Scholar</a></div><div class="crossref-doi js-ref-link"><a class="openInAnotherWindow" href="http://dx.doi.org/10.1063/1.1743957" target="_blank">Crossref</a></div><div class="adsDoiReference hide"><a class="openInAnotherWindow" href="http://adsabs.harvard.edu/cgi-bin/basic_connect?qsearch=10.1063%2F1.1743957" target="_blank">Search ADS</a></div><div class="xslopenurl empty-target"><span class="inst-open-url-holders" data-targetId="10.1063%2F1.1743957"> </span></div> </div></div></div></div></div><div data-content-id="c6" xmlns:helper="urn:XsltStringHelper"><div class="ref false"><div class="ref-content "><span class="label title-label">6.</span><div class="citation mixed-citation"><span class="name string-name"><div class="given-names">W. W.</div> <div class="surname">Wood</div></span> and <span class="name string-name"><div class="given-names">J. D.</div> <div class="surname">Jacobson</div></span>, <div class="source">J. Chem. 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W.</div> <div class="surname">Wood</div></span>, in <div class="source">The Monte Carlo Method in the Physical Sciences</div>, edited by <span class="person-group"><span class="name string-name"><div class="given-names">J. E.</div> <div class="surname">Gubernatis</div></span></span> (<div class="publisher-name">American Institute of Physics</div>, New York, <div class="year">2003</div>), p. <div class="fpage">39</div>, and references therein.<div class="citation-links"><div class="google-scholar-ref-link js-ref-link"><a href="https://scholar.google.com/scholar_lookup?title=The%20Monte%20Carlo%20Method%20in%20the%20Physical%20Sciences&author=W.%20W.%20Wood&author=J.%20E.%20Gubernatis&publication_year=2003&book=The%20Monte%20Carlo%20Method%20in%20the%20Physical%20Sciences" target="_blank">Google Scholar</a></div> </div></div></div></div></div><div data-content-id="c8" xmlns:helper="urn:XsltStringHelper"><div class="ref false"><div class="ref-content "><span class="label title-label">8.</span><div class="citation mixed-citation"><div class="source">Symposium on Monte Carlo Methods</div>, edited by <span class="person-group"><span class="name string-name"><div class="given-names">H. 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E.</div> <div class="surname">Gubernatis</div></span></span> (<div class="publisher-name">American Institute of Physics</div>, New York, <div class="year">2003</div>), p. <div class="fpage">32</div>.<div class="citation-links"><div class="google-scholar-ref-link js-ref-link"><a href="https://scholar.google.com/scholar_lookup?title=The%20Monte%20Carlo%20Method%20in%20the%20Physical%20Sciences&author=M.%20N.%20Rosenbluth&author=J.%20E.%20Gubernatis&publication_year=2003&book=The%20Monte%20Carlo%20Method%20in%20the%20Physical%20Sciences" target="_blank">Google Scholar</a></div> </div></div></div></div></div><div data-content-id="c10" xmlns:helper="urn:XsltStringHelper"><div class="ref false"><div class="ref-content "><span class="label title-label">10.</span><div class="citation mixed-citation"><span class="name string-name"><div class="given-names">R.</div> <div class="surname">Gupta</div></span>, in <div class="source">The Monte Carlo Method in the Physical Sciences</div>, edited by <span class="person-group"><span class="name string-name"><div class="given-names">J. 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