{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.topic/1","content_sha256":"f62e7c086ed76c28d1eb4211850d9e118fff2a6d5e854605621fe818546e1212","created":"2026-10-03T07:17:52Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":[],"salt":"70f09b38d29c0524a3fa4281968e312d88d1f12c05069eaef8c6fd52bb448cef","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"topic"},"content":{"external_id":"mathph.sigma-models","field":"mathph","n":"1","review_cite":"A. M. Polyakov, Interaction of Goldstone particles in two dimensions. Applications to ferromagnets and massive Yang-Mills fields, Physics Letters B 59, 1975","review_link":"https://doi.org/10.1016/0370-2693(75)90161-6","review_verified":"true","summary":"The O(N) model describes arrows of fixed length on a grid, each with N components, that prefer to point the same way as their neighbours. In two dimensions physicists predict that for N of three or more the alignment is always lost beyond a finite distance, however cold the system is, but nobody has proven it.","title":"Mass gap in two-dimensional sigma models","topic_ref":null,"why":"It is the simplest test case for asymptotic freedom and dynamical mass generation, the mechanism behind the expected four-dimensional Yang-Mills mass gap."},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b4bb48d722ff2368d355af570ae350e795f3cc5cea7a0142509f239da3c98279","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"f6bf85a358edc37a42f8427fbaaf3ba791bab8d802150b8bfcf2b8420e00c403","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"8tCBCc9pnUDqaWPxykujsnPPAA6KnP60UquPc5rEdotO9CHDwFymWH7ztT5kK0kgwhAmZmruYkTkBGMckUGFAg"},"schema":"pubphys.envelope/1"},"record_hash":"b4bb48d722ff2368d355af570ae350e795f3cc5cea7a0142509f239da3c98279","leaf_index":266}