{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T17:57:38Z","timestamp":1770573458407,"version":"3.49.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T00:00:00Z","timestamp":1554076800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T00:00:00Z","timestamp":1555459200000},"content-version":"vor","delay-in-days":16,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. High Energ. Phys."],"published-print":{"date-parts":[[2019,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current \u2014 a non-conserved vector operator of dimension exactly (<jats:italic>d<\/jats:italic> \u2212 1), whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound \u0394<jats:sub>\n              <jats:italic>V<\/jats:italic>\n            <\/jats:sub> &gt; 5.0 on the scaling dimension of the lowest virial current candidate <jats:italic>V<\/jats:italic>, well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model.<\/jats:p>","DOI":"10.1007\/jhep04(2019)115","type":"journal-article","created":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T09:27:51Z","timestamp":1555579671000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A structural test for the conformal invariance of the critical 3d Ising model"],"prefix":"10.1007","volume":"2019","author":[{"given":"Sim\u00e3o","family":"Meneses","sequence":"first","affiliation":[]},{"given":"Jo\u00e3o","family":"Penedones","sequence":"additional","affiliation":[]},{"given":"Slava","family":"Rychkov","sequence":"additional","affiliation":[]},{"given":"J. M.","family":"Viana Parente Lopes","sequence":"additional","affiliation":[]},{"given":"Pierre","family":"Yvernay","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,4,17]]},"reference":[{"key":"10401_CR1","volume":"D 86","author":"S El-Showk","year":"2012","unstructured":"S. El-Showk et al., Solving the 3D Ising model with the conformal bootstrap, Phys. Rev.\n                           D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].","journal-title":"Phys. Rev."},{"key":"10401_CR2","doi-asserted-by":"crossref","unstructured":"S. El-Showk et al., Solving the 3d Ising model with the conformal bootstrap II. c-minimization and precise critical exponents, J. Stat. Phys.\n                           157 (2014) 869 [arXiv:1403.4545] [INSPIRE].","DOI":"10.1007\/s10955-014-1042-7"},{"key":"10401_CR3","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/JHEP11(2014)109","volume":"11","author":"F Kos","year":"2014","unstructured":"F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping mixed correlators in the 3D Ising model, JHEP\n                           11 (2014) 109 [arXiv:1406.4858] [INSPIRE].","journal-title":"JHEP"},{"key":"10401_CR4","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1007\/JHEP06(2015)174","volume":"06","author":"D Simmons-Duffin","year":"2015","unstructured":"D. Simmons-Duffin, A semidefinite program solver for the conformal bootstrap, JHEP\n                           06 (2015) 174 [arXiv:1502.02033] [INSPIRE].","journal-title":"JHEP"},{"key":"10401_CR5","doi-asserted-by":"publisher","first-page":"036","DOI":"10.1007\/JHEP08(2016)036","volume":"08","author":"F Kos","year":"2016","unstructured":"F. Kos, D. Poland, D. Simmons-Duffin and A. 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Bill\u00f3 et al., Line defects in the 3d Ising model, JHEP\n                           07 (2013) 055 [arXiv:1304.4110] [INSPIRE].","journal-title":"JHEP"},{"key":"10401_CR8","doi-asserted-by":"publisher","first-page":"022","DOI":"10.1007\/JHEP08(2015)022","volume":"08","author":"C Cosme","year":"2015","unstructured":"C. Cosme, J.M. V.P. Lopes and J. Penedones, Conformal symmetry of the critical 3D Ising model inside a sphere, JHEP\n                           08 (2015) 022 [arXiv:1503.02011] [INSPIRE].","journal-title":"JHEP"},{"key":"10401_CR9","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2015\/07\/P07014","volume":"1507","author":"G Gori","year":"2015","unstructured":"G. Gori and A. Trombettoni, Conformal invariance in three dimensional percolation, J. Stat. Mech.\n                           1507 (2015) P07014 [arXiv:1504.07209] [INSPIRE].","journal-title":"J. Stat. 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