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The ground state has a thermodynamic degeneracy at $J'$=0, and I have studied lattice symmetry breaking associated to lifting this degeneracy. Third-order perturbation in $J'$ for general spin $S$ shows that the effective Hamiltonian has a form of three-tetrahedron interactions of pseudospins $\\tau$, which is identical to that previously derived for $S$=1/2, and I have calc"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.04468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-02-15T06:01:13Z","cross_cats_sorted":[],"title_canon_sha256":"85067421c8631ac9d147f85e0189ca914986abacfc805aedacee04d3635ea43f","abstract_canon_sha256":"abae3a0dbc8595f2c7a80657032998eeedfe5f948a7cafeade11bd7dc68172f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:41.624904Z","signature_b64":"7CPWdyyBuYqeDU8LR07oQrtwUhY7FdrtSR+DLXC7IlhpEGkBTcn76ayxZR6YOwlqbga3ctMbeftb9VvrRfIVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48fe8aa68ddd17f86aaf8e3d4ac637104de17b1085a79a649436383a973802e9","last_reissued_at":"2026-05-18T00:50:41.624147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:41.624147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Theory of antiferromagnetic Heisenberg spins on breathing pyrochlore lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Hirokazu Tsunetsugu","submitted_at":"2017-02-15T06:01:13Z","abstract_excerpt":"Spin-singlet orders are studied for the antiferromagnetic Heisenberg model with spin $S$>1/2 on a breathing pyrochlore lattice, where tetrahedron units are weakly coupled and exchange constants have two values $0<J' \\ll J$. 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