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Rev. Lett."],"accepted":{"date-parts":[[2026,8,12]]},"abstract":"<jats:p>Sampling equilibrium configurations of three-dimensional (3D) spin glasses with quenched disorder remains a fundamental challenge in statistical physics. The rugged energy landscape, pronounced critical slowing down, and intrinsic ergodicity breaking render standard Monte\u00a0Carlo methods severely inefficient, particularly for large systems at low temperatures. In this Letter, we introduce the tensor-network Markov-chain Monte\u00a0Carlo (TNMCMC) approach to address the issue. By formulating large-scale collective updates via tensor-network contractions on 2D lattice slices, TNMCMC yields unbiased samples of the Boltzmann distribution while substantially reducing autocorrelation times relative to conventional MCMC approaches. Numerical benchmarks on 3D spin glasses demonstrate that the method systematically mitigates critical slowing down. Furthermore, application to three- and four-state 3D Potts models shows that TNMCMC can traverse the exponential free-energy barriers of first-order phase transitions that typically hinder local MC updates. These results establish TNMCMC as a promising numerical framework capable of addressing important 3D problems in statistical physics and beyond, such as the precise computation of low-temperature thermodynamic properties of three-dimensional spin glasses and the decoding of quantum error-correcting codes with a three-dimensional topology.<\/jats:p>","DOI":"10.1103\/96lr-z7tb","type":"journal-article","created":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T12:11:57Z","timestamp":1786536717000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Tensor-Network Markov-Chain Monte\u00a0Carlo: Efficient Sampling of Three-Dimensional Spin Glasses"],"prefix":"10.1103","volume":"137","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-6940-2934","authenticated-orcid":true,"given":"Tao","family":"Chen","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04c4dkn09","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Science and Technology of China"},{"id":[{"id":"https:\/\/ror.org\/04c4dkn09","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2629-4695","authenticated-orcid":true,"given":"Jing","family":"Liu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04w9fbh59","id-type":"ROR","asserted-by":"publisher"}],"name":"Beijing University of Posts and Telecommunications"},{"id":[{"id":"https:\/\/ror.org\/02xtbq882","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute of Theoretical Physics"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Youjin","family":"Deng","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04c4dkn09","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Science and Technology of China"},{"id":[{"id":"https:\/\/ror.org\/04c4dkn09","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Science and Technology of China"},{"id":[{"id":"https:\/\/ror.org\/02wmsc916","id-type":"ROR","asserted-by":"publisher"}],"name":"Guizhou University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8496-2730","authenticated-orcid":true,"given":"Pan","family":"Zhang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02xtbq882","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute of Theoretical Physics"},{"id":[{"id":"https:\/\/ror.org\/05qbk4x57","id-type":"ROR","asserted-by":"publisher"}],"name":"UCAS"},{"id":[{"id":"https:\/\/ror.org\/04c4dkn09","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Science and Technology of China"},{"id":[{"id":"https:\/\/ror.org\/05qbk4x57","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,9,9]]},"reference":[{"key":"96lr-z7tbCc1R1","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4608\/5\/5\/017","type":"journal-article"},{"key":"96lr-z7tbCc2R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.58.801","type":"journal-article"},{"key":"96lr-z7tbCc3R1","volume-title":"Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology","author":"A. 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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":"117101"}}