{"paper":{"title":"Chaitin Phase Transition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"James Purcell, Toby Cubitt, Zhi Li","submitted_at":"2024-10-03T15:41:39Z","abstract_excerpt":"We construct a family of Hamiltonians whose phase diagram is guaranteed to have a single phase transition, yet the location of this phase transition is uncomputable. The Hamiltonians $H(\\phi)$ describe qudits on a two-dimensional square lattice with translationally invariant, nearest-neighbour interactions tuned by a continuous parameter $\\phi\\in(0,1]$. For all $\\phi\\in(0,1]$, $H(\\phi)$ is in one of two phases, one a gapless phase, the other a gapped phase. The phase transition occurs when $\\phi$ equals the Chaitin's constant $\\Omega$, a well-defined real number that encodes the Halting proble"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.02600","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.02600/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}