{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"50167fe69d2be46af262b6389c640c90b09abe353cca4ff17f260a7093cf73e7","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["9dfbcd8664ca32ee13a40a590654b4819b04ddae1ca26862f1866d4c5dc1bba9","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"d9d304c898b67979434b03c9e9d90c34f6780f099aac8d81b6dde45b6fc3cb13","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":["ai:gpt-5.5"],"external_id":"cm.spin-ice.photon-heat-capacity","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Emergent photons should add a heat capacity growing as the cube of temperature, like lattice vibrations, with a size fixed by the photon speed. Measuring it and matching the speed predicted from the measured interactions would be a sharp test.","posed_since":"","precise":"In quantum spin ice the photon speed $c$ is set by the ring-exchange scale $g=12J_{\\mathrm{pm}}^{3}/J_{\\mathrm{zz}}^{2}$ ($c \\sim g$ $a$$/\\hbar$ up to a computed prefactor, a the lattice spacing), and the photon heat capacity per volume is $C/V = (4 \\pi^{2}/15) k_{\\mathrm{B}} (k_{\\mathrm{B}} T/\\hbar c)^{3}$ for two polarizations. Measure $C/T^{3}$ below the photon bandwidth in a candidate material and compare $c$ with the value from independently fitted exchange parameters. An answer is $c$ measured and predicted, with agreement or disagreement within errors.","problem_ref":"9dfbcd8664ca32ee13a40a590654b4819b04ddae1ca26862f1866d4c5dc1bba9","references":"","settled_by":"Heat capacity below about 0.05 K with nuclear and phonon contributions subtracted, compared with the photon speed from neutron spectra and quantum Monte Carlo.","status_note":"","title":"Measure the emergent-photon $T^3$ heat capacity and speed in quantum spin ice","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3083796242547fc940b28fce1c0bda3a4003ef508ede76ac3eb5bf0c9771ed84","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"b3b13f83c76487049064c1a424fd4ffa4a1aea580f2c76e3e60e8dd405b9ae25","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"EnlxKS5Vzy3-jz6UCsyme-U4vHky-i-0nJBZ1RjMynwv_h6ucw-w4LkVcLKbPaDjS0Z86EEbCv-4ebQi87PABQ"},"schema":"pubphys.envelope/1"},"record_hash":"3083796242547fc940b28fce1c0bda3a4003ef508ede76ac3eb5bf0c9771ed84","leaf_index":3048}