{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:07:08Z","timestamp":1790726828678,"version":"4.1.0"},"reference-count":34,"publisher":"American Physical Society (APS)","issue":"22","license":[{"start":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T00:00:00Z","timestamp":1780358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["560547547"],"award-info":[{"award-number":["560547547"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["JA 483\/36-1"],"award-info":[{"award-number":["JA 483\/36-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010579","name":"Deutsch-Franz\u00f6sische Hochschule","doi-asserted-by":"publisher","award":["CDFA-02-07"],"award-info":[{"award-number":["CDFA-02-07"]}],"id":[{"id":"10.13039\/501100010579","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2026,4,10]]},"abstract":"<jats:p>\n                    We propose a fast and general predecision scheme for Metropolis Monte\u00a0Carlo simulation of\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <a:mrow>\n                        <a:mi>d<\/a:mi>\n                      <\/a:mrow>\n                    <\/a:math>\n                    -dimensional long-range interacting lattice models with\n                    <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <c:mrow>\n                        <c:mi>N<\/c:mi>\n                      <\/c:mrow>\n                    <\/c:math>\n                    constituents. For potentials of the form\n                    <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <e:mrow>\n                        <e:mi>V<\/e:mi>\n                        <e:mo stretchy=\"false\">(<\/e:mo>\n                        <e:mi>r<\/e:mi>\n                        <e:mo stretchy=\"false\">)<\/e:mo>\n                        <e:mo>=<\/e:mo>\n                        <e:msup>\n                          <e:mrow>\n                            <e:mi>r<\/e:mi>\n                          <\/e:mrow>\n                          <e:mrow>\n                            <e:mo>\u2212<\/e:mo>\n                            <e:mi>d<\/e:mi>\n                            <e:mo>\u2212<\/e:mo>\n                            <e:mi>\u03c3<\/e:mi>\n                          <\/e:mrow>\n                        <\/e:msup>\n                      <\/e:mrow>\n                    <\/e:math>\n                    , this reduces the computational complexity from\n                    <i:math xmlns:i=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <i:mrow>\n                        <i:mi>O<\/i:mi>\n                        <i:mrow>\n                          <i:mo stretchy=\"false\">(<\/i:mo>\n                          <i:msup>\n                            <i:mrow>\n                              <i:mi>N<\/i:mi>\n                            <\/i:mrow>\n                            <i:mrow>\n                              <i:mn>2<\/i:mn>\n                            <\/i:mrow>\n                          <\/i:msup>\n                          <i:mo stretchy=\"false\">)<\/i:mo>\n                        <\/i:mrow>\n                      <\/i:mrow>\n                    <\/i:math>\n                    to\n                    <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <m:mrow>\n                        <m:mi>O<\/m:mi>\n                        <m:mrow>\n                          <m:mo stretchy=\"false\">(<\/m:mo>\n                          <m:msup>\n                            <m:mrow>\n                              <m:mi>N<\/m:mi>\n                            <\/m:mrow>\n                            <m:mrow>\n                              <m:mn>2<\/m:mn>\n                              <m:mo>\u2212<\/m:mo>\n                              <m:mi>\u03c3<\/m:mi>\n                              <m:mo>\/<\/m:mo>\n                              <m:mi>d<\/m:mi>\n                            <\/m:mrow>\n                          <\/m:msup>\n                          <m:mo stretchy=\"false\">)<\/m:mo>\n                        <\/m:mrow>\n                      <\/m:mrow>\n                    <\/m:math>\n                    for\n                    <q:math xmlns:q=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <q:mrow>\n                        <q:mi>\u03c3<\/q:mi>\n                        <q:mo>&lt;<\/q:mo>\n                        <q:mi>d<\/q:mi>\n                      <\/q:mrow>\n                    <\/q:math>\n                    and to\n                    <s:math xmlns:s=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <s:mrow>\n                        <s:mi>O<\/s:mi>\n                        <s:mrow>\n                          <s:mo stretchy=\"false\">(<\/s:mo>\n                          <s:mi>N<\/s:mi>\n                          <s:mo stretchy=\"false\">)<\/s:mo>\n                        <\/s:mrow>\n                      <\/s:mrow>\n                    <\/s:math>\n                    for\n                    <w:math xmlns:w=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <w:mrow>\n                        <w:mi>\u03c3<\/w:mi>\n                        <w:mo>&gt;<\/w:mo>\n                        <w:mi>d<\/w:mi>\n                      <\/w:mrow>\n                    <\/w:math>\n                    , respectively. The algorithm is implemented and tested for several\n                    <y:math xmlns:y=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <y:mrow>\n                        <y:mi mathvariant=\"normal\">O<\/y:mi>\n                        <y:mo stretchy=\"false\">(<\/y:mo>\n                        <y:mi>n<\/y:mi>\n                        <y:mo stretchy=\"false\">)<\/y:mo>\n                      <\/y:mrow>\n                    <\/y:math>\n                    spin models ranging from the Ising over the\n                    <db:math xmlns:db=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <db:mi>X<\/db:mi>\n                      <db:mi>Y<\/db:mi>\n                    <\/db:math>\n                    to the Edwards-Anderson spin-glass model. With the same random-number sequence it produces exactly the same Markov chain as a simulation with explicit summation of all terms in the Hamiltonian. Because of its generality, its simplicity, and its reduced computational complexity it has the potential to find broad application and thus lead to a deeper understanding of the role of long-range interactions in the physics of lattice models, especially in nonequilibrium settings.\n                  <\/jats:p>","DOI":"10.1103\/29yw-9grr","type":"journal-article","created":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T19:16:00Z","timestamp":1775848560000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Efficient Predecision Scheme for Metropolis Monte\u00a0Carlo Simulation of Long-Range Interacting Lattice Systems"],"prefix":"10.1103","volume":"136","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7699-9178","authenticated-orcid":true,"given":"Fabio","family":"M\u00fcller","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03s7gtk40","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e4t Leipzig"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5165-9097","authenticated-orcid":true,"given":"Wolfhard","family":"Janke","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03s7gtk40","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e4t Leipzig"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,6,2]]},"reference":[{"key":"29yw-9grrCc1R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1699114","type":"journal-article"},{"key":"29yw-9grrCc2R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.71.847","type":"journal-article"},{"key":"29yw-9grrCc3R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511780516","type":"book","volume-title":"A Kinetic View of Statistical Physics","author":"P.\u2009L. 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imperfect ordering in |Ji,j|, where subsequences are additionally ordered to minimize cache misses, can lead to further improved wall-clock times.","type":"other"},{"key":"29yw-9grrCc19R1","unstructured":"We have carefully checked that, compared to a simple Metropolis implementation, the increase of the algorithmic prefactor stemming from the slightly more complicated algorithmic procedure is of the order of unity and thus negligible.","type":"other"},{"key":"29yw-9grrCc20R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/29yw-9grr where the computational complexity of the new method is derived under minimal assumptions and a full implementation of the algorithm in the julia programming language is provided.","type":"other"},{"key":"29yw-9grrCc20R2","unstructured":"The code can also be downloaded from 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All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"227101"}}