{"paper":{"title":"Phase Ordering in a few O(n) Symmetric Models: Slow Growth, Mpemba Effect and Experimental Relevance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"In the 3D XY model, characteristic length grows as t to the 0.15 after zero-temperature quench because vortex cores form line defects whose annihilation sets the pace, and quenches from higher starting temperatures reach equilibrium faster.","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Nalina Vadakkayil, Sohini Chatterjee, Subir K. Das, Wasim Akram","submitted_at":"2026-05-13T14:04:28Z","abstract_excerpt":"We study phase ordering dynamics in the three-dimensional nonconserved XY model, via Monte Carlo simulations, for quenches from paramagnetic phase to certain final temperatures $T_f$ within the ferromagnetic region of the phase diagram. The growth in the system occurs via annihilation of vortex and anti-vortex pairs, cores of which, in the three dimensional system geometry, join from different planes, on which the spins lie, to form line defects. In the long-time limit, the associated characteristic length scale, $\\ell(t)$, appears to grow with time $(t)$ approximately as $t^{0.15}$, for $T_f="},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In the long-time limit, the associated characteristic length scale, ℓ(t), appears to grow with time (t) approximately as t^{0.15}, for Tf=0. The exponent is much smaller... than 1/2... We carry out quenches from different starting temperatures, Ts... It is observed that the systems with higher Ts approach the final equilibrium faster. This resembles the puzzling Mpemba effect.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The identification of line defects formed by vortex cores joining across planes and the assumption that their annihilation directly sets the measured growth exponent without significant finite-size or lattice artifacts dominating the long-time regime.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Simulations find slow t^0.15 growth in 3D XY phase ordering at zero temperature and Mpemba-like faster equilibration from higher initial temperatures in XY and Ising models.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In the 3D XY model, characteristic length grows as t to the 0.15 after zero-temperature quench because vortex cores form line defects whose annihilation sets the pace, and quenches from higher starting temperatures reach equilibrium faster.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a4f01c022b80c157fe03fb8de74a2dacf51bbbbdb04e75adc977e1e825fb47b7"},"source":{"id":"2605.13564","kind":"arxiv","version":1},"verdict":{"id":"b11d0c75-c3d6-4ac3-8a7c-78d61a1c65db","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:54:39.909238Z","strongest_claim":"In the long-time limit, the associated characteristic length scale, ℓ(t), appears to grow with time (t) approximately as t^{0.15}, for Tf=0. The exponent is much smaller... than 1/2... We carry out quenches from different starting temperatures, Ts... It is observed that the systems with higher Ts approach the final equilibrium faster. This resembles the puzzling Mpemba effect.","one_line_summary":"Simulations find slow t^0.15 growth in 3D XY phase ordering at zero temperature and Mpemba-like faster equilibration from higher initial temperatures in XY and Ising models.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The identification of line defects formed by vortex cores joining across planes and the assumption that their annihilation directly sets the measured growth exponent without significant finite-size or lattice artifacts dominating the long-time regime.","pith_extraction_headline":"In the 3D XY model, characteristic length grows as t to the 0.15 after zero-temperature quench because vortex cores form line defects whose annihilation sets the pace, and quenches from higher starting temperatures reach equilibrium faster."},"references":{"count":77,"sample":[{"doi":"","year":1969,"title":"E. B. Mpemba and D. G. Osborne, Cool?, Phys. Educ. 4, 172 (1969)","work_id":"213447ea-33c5-4ff7-ac6f-e547a48e8c9b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Z. Tang, W. Huang, Y. Zhang, Y. Liu, and L. Zhao, Direct obs ervation of the Mpemba effect with water: Probe the mysterious heat transfer, InfoMat 5, e12352 (2023) . 12","work_id":"e93a63df-45a4-4e39-ab2e-29d9fb089f01","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"H. C. Burridge and O. Hallstadius, Observing the Mpemba e ffect with minimal bias and the value of the Mpemba effect to scientific outreach and engagement, Proc. R. Soc. A 476, 20190829 (2020)","work_id":"c4e61bfb-0a04-49a5-aa17-44508111fb32","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"S. Ghosh, P. Pathak, S. Chatterjee, and S. K. Das, Simulat ions of Mpemba effect in water and Lennard-Jones models, Commun. Phys. 8, 359 (2025)","work_id":"83d0a983-afb8-40e3-afb0-445b21ab655d","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2026,"title":"G. Teza, J. Bechhoefer, A. Lasanta, O. Raz, and M. Vucelja , Speedups in nonequilibrium thermal relaxation: Mpemba and related effects, Phys. Rep. 1164, 1 (2026)","work_id":"7a8e6e8d-0357-4b0d-8c3f-219cadcd0c70","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":77,"snapshot_sha256":"ea0f1ceba0bf71d3eebaecd04409fe9a4293e0face33e54b3d1ac4b422497e4c","internal_anchors":1},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}