{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b348f8b21515d24a09c815e9366fbba375776124e3a26ba2f70c5079bff8e776","created":"2026-10-03T07:18:01Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","692e84275354594b030e926ee9b76c7f88ecf4490783f075252d14127adb8d67"],"salt":"91e4f55129d9cc57ee87a27a2d7b43e6ceef42e94f5c0c7adb558f3af2ea947c","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cm.spin-ice.photon-heat-capacity","kind":"well-posed","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"692e84275354594b030e926ee9b76c7f88ecf4490783f075252d14127adb8d67","relation":"special_case"}],"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 ~ 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_B (k_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":null,"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":"52cddd9c3d75748e46e41f34a20edd20c81c928cc0056fa7e4de59ade0220e82"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9dfbcd8664ca32ee13a40a590654b4819b04ddae1ca26862f1866d4c5dc1bba9","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"da19f83d81012b9f2106858fa51e3444514d25d034125e202c4b467f8f6fb937","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"Z8RvBPUYbAmV-9A9vU7OIdoL5iCN3k6NyBiiAgEAcKbqdgG9InuygXzmRR1Wa0ynkMXLfZZ2EBM4REI75wXLBw"},"schema":"pubphys.envelope/1"},"record_hash":"9dfbcd8664ca32ee13a40a590654b4819b04ddae1ca26862f1866d4c5dc1bba9","leaf_index":1172}