{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"88983e0d0f8565a996185781dbf5d9ee7bfe4ab95712f6f713c4ae2fa166e5ec","created":"2026-10-03T07:18:01Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"9634e1a7ece38db089f7667b97e52ddd7033e348386043632a398d6745d748ce","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cm.wigner-crystal-2d.critical-rs-jellium","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Computer simulations predict the electron sheet crystallizes once repulsion exceeds kinetic energy by a factor of roughly 30 to 40, but the exact threshold and whether the change is abrupt are not pinned down.","posed_since":"","precise":"For the 2D homogeneous electron gas with $1/r$ repulsion and a uniform neutralizing background at $T = 0$, determine the critical r_s_c for the liquid to triangular Wigner crystal transition, whether it is first order, and the spin state of each phase. Diffusion Monte Carlo gave r_s_c ~ 37 (Tanatar and Ceperley 1989), $31 \\pm 1$ (Drummond and Needs 2009) and $35 \\pm 1$ with no stable ferromagnetic fluid (Azadi, Drummond and Vinko 2024, Physical Review B 110, 245145); an answer is r_s_c with controlled fixed-node and finite-size errors.","problem_ref":null,"references":"","settled_by":"A calculation with controlled nodal error (for example neural-network variational wavefunctions benchmarked against released-node or auxiliary-field results) at sizes that allow a thermodynamic extrapolation.","status_note":"Fixed-node diffusion Monte Carlo estimates differ by more than their quoted errors ($31 \\pm 1$ in 2009, $35 \\pm 1$ in 2024), so nodal and finite-size errors are not under control.","title":"Critical density for Wigner crystallization of the clean 2D electron gas","topic_ref":"0172a4875504d269442a9c602dc559b0e1b689d7513bab808338a3559e713e6c"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"39ffdace15de585ca3a5319a748b29844126488345a507125efac895fce1639b","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"59d19588e0d91c0cc52022a8fe594306089cead06fa0366958fe40a53d65a10b","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"olxdPcXCgSGX9qdDHsztTaeyFaSUUkYdaLBPB1Rl9ugCFlUKeEEGgy5M9wMhPMSlVXEFSvSgo6zod1uj04hVAQ"},"schema":"pubphys.envelope/1"},"record_hash":"39ffdace15de585ca3a5319a748b29844126488345a507125efac895fce1639b","leaf_index":1218}