{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5f2e8608cf3a8e9e6e4123716657398f97528d297220c89ce93470c7f1d06331","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"4031965fd1c84278f86740b38c8274160bca7d83ee10148b4b0a301ec349643c","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.quantum-spin-gaps.neel-spin-half","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"In the ground state of a square grid of spin-$1/2$ magnets with antiparallel coupling, the spins should line up in a checkerboard pattern with finite strength. This is proven for larger spins but not for spin $1/2$.","posed_since":"","precise":"H = sum_<ij> S_i . S_j on $Z^2$ with $S = 1/2$. Prove long-range order in the ground state: the staggered magnetization $m_s = \\lim \\sqrt{\\langle(1/N \\sum_x (-1)^x S_x)^2\\rangle}$ is positive (numerically $m_s$ approximately 0.307). Answer: a proof.","problem_ref":null,"references":"","settled_by":"A proof of positive staggered magnetization, for example by sharpening reflection-positivity bounds.","status_note":"Proven by reflection positivity for $S \\ge 1$ in 2D (Neves and Perez, 1986; Kennedy, Lieb and Shastry, 1988) and for $S = 1/2$ in 3D (Kennedy, Lieb and Shastry, 1988).","title":"Neel order in the spin-$1/2$ square-lattice Heisenberg antiferromagnet","topic_ref":"2277c2056f9b4652a96eb984886b4114703ad1bdf3de5eaf3cbb73c0aab421ae"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ede4961a119c4dfb0a22350fe868db8dc11087a0f4604ae4c3bf571274310693","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"4718cfe0ac70f111a541a05df83c06a9ece90e286f2abb0ca0a5bf1ab3dc6e8c","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"UVbhXt-kc-zOokYQz08me8QsOBUzzf0UaW8FtzmgpWFym2GO3CthB54ZGlUWThhs85OWAP0phCfAAsdQNJ1qDQ"},"schema":"pubphys.envelope/1"},"record_hash":"ede4961a119c4dfb0a22350fe868db8dc11087a0f4604ae4c3bf571274310693","leaf_index":1655}