{"paper":{"title":"The random geometry of equilibrium phases","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"C. Maes, H.-O. Georgii, O. H\\\"aggstr\\\"om","submitted_at":"1999-05-05T16:41:13Z","abstract_excerpt":"This is a (long) survey about applications of percolation theory in equilibrium statistical mechanics. The chapters are as follows:\n 1. Introduction\n 2. Equilibrium phases\n 3. Some models\n 4. Coupling and stochastic domination\n 5. Percolation\n 6. Random-cluster representations\n 7. Uniqueness and exponential mixing from non-percolation\n 8. Phase transition and percolation\n 9. Random interactions\n 10. Continuum models"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9905031","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":""},"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"}