{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"735defbe4154d292948324cfa0b89d5efc04b09e56d6d53e65de0568d9e293e2","created":"2026-10-03T07:17:59Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"249c1f7e3b5a629f5da0ef4ad8a899cc739dc42f58cdc08691c746214edacd88","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"cm.deconfined-criticality.neel-vbs-order","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"In the J-Q model a magnetic (Neel) state turns into a state of locked spin pairs (a valence-bond solid) as a four-spin coupling grows. Simulations show slowly drifting critical exponents, so it is unclear whether the transition is continuous or a very weak jump.","posed_since":"2004","precise":"Square-lattice $S = 1/2$ $J-Q$ model, $H = -J \\sum P_{ij} - Q \\sum P_{ij} P_{kl}$ with $P_{ij}$ the singlet projector, at the Neel to columnar-VBS transition $q_c = (Q/J)_c$. Determine whether both order parameters vanish continuously at $q_c$ or remain finite (first order), and if first order, the coexisting order parameters and the correlation length at $q_c$. An answer is the thermodynamic-limit order parameters at $q_c$ with error bars.","problem_ref":null,"references":"","settled_by":"Quantum Monte Carlo on lattices beyond $L = 256$, or a controlled extrapolation, showing nonzero coexisting Neel and VBS order at $q_c$, or their vanishing.","status_note":"2024 to 2026 quantum Monte Carlo and spectroscopic studies (for example arXiv:2512.11329) report evidence for a weakly first-order transition with emergent SO(5) symmetry broken to O(4).","title":"Is the Neel to valence-bond-solid transition in the J-Q model 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