{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"eaa793dbe5714f9fb3a3349cae7c60ff1c75cd5339046753faa6a923a222364a","created":"2026-10-03T07:18:05Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"b56182ced65db24d3a68aabe8ba86a30c54a69f9f26b33d7095db913aac33f18","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"mathph.crystal-order-temperature.hexatic-phase","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Theory predicts that 2D crystals melt in two steps through an intermediate hexatic phase, in which bond directions stay aligned while positions are disordered as in a liquid. Prove such a phase exists for some particle system.","posed_since":"1978","precise":"For hard disks or a 2D system with smooth repulsion, prove existence of a range of $(T, \\rho)$ where positional correlations decay exponentially while bond-orientational correlations $\\langle\\psi_6(x)\\,\\psi_6(0)*\\rangle$ decay as a power law, as in the Kosterlitz-Thouless-Halperin-Nelson-Young melting scenario. Hard-disk simulations (Bernard, Krauth 2011) find a hexatic phase near packing fraction 0.70 to 0.72 with a first-order liquid-hexatic transition.","problem_ref":null,"references":"","settled_by":"A proof of the two distinct decay laws in a nonempty parameter region of a 2D continuum model.","status_note":"","title":"Existence of a hexatic phase between 2D solid and liquid","topic_ref":"ea8bde04090399eb2ce07a2138c4a5deafce80c26031655b989bc3381e0879d5"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"65a9f0f5ad9e1e569866bf3836c7354dd73f97dbac03d7fbc3590bb1bc9c9c23","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"7491ad7a7fbc30dcf7e0f59be2190695e1299e5f28eca838ee483389681bc4f5","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"iwEL_q6pwyPeLfZqwoFiCa0Eebo80clQZY1GOzMYaxrqGcsbkTG1iSglNlDcg9h4MpXlLnP3HJKsrGSzinKGBA"},"schema":"pubphys.envelope/1"},"record_hash":"65a9f0f5ad9e1e569866bf3836c7354dd73f97dbac03d7fbc3590bb1bc9c9c23","leaf_index":1604}