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Here $\\langle x, y \\rangle \\in E $, i.e. $x$ and $y$ are neighbors in $Z^d$. The intensities $J_{xy}$ and the spins $\\sigma (x) , \\sigma (y)$ are arbitrary real. To control their growth we introduce appropriate sets $J_q\\subset R^E$ and $S_p\\subset R^{Z^d}$ and prove that for every $J = (J_{xy}) \\in J_q$: (a) the set of Gibbs measures $G_p(J)= \\{\\mu: solves DLR, \\mu(S_p)=1\\}$ is non-void and weakly compact; (b) each $\\mu\\inG_p(J)$ obeys an integrability estimate, the same f","authors_text":"Tanja Pasurek, Yuri Kondratiev, Yuri Kozitsky","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-16T15:16:24Z","title":"Gibbs measures of disordered lattice systems with unbounded spins"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2686","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4fc88f9d12a07a3a686135f2d43e50e879dbaf16fe75f47a4b6d71d6013576ae","target":"record","created_at":"2026-05-18T04:42:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4cc1b6446f261c756c2b77f1ae66ee6833a8deacefa9e5d1d1ad9056d5dec878","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-16T15:16:24Z","title_canon_sha256":"2825d44fa875affd5a1f76be69f18224660f78e3d0d8ff626748c0871431dc9a"},"schema_version":"1.0","source":{"id":"1008.2686","kind":"arxiv","version":1}},"canonical_sha256":"3132a6643ca4820b154355a0ec7352a2eb406d5b433510b9c18b85ffaecb608a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3132a6643ca4820b154355a0ec7352a2eb406d5b433510b9c18b85ffaecb608a","first_computed_at":"2026-05-18T04:42:12.779970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:12.779970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mRkV1o4I/FeQ0z9+tc2RFOBoNSudg/he+ef4DuAPl6aBSkiJGNy48Nhzbxrgnm/5c2PutXMThBfsHj3hT7LxBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:12.780666Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fc88f9d12a07a3a686135f2d43e50e879dbaf16fe75f47a4b6d71d6013576ae","sha256:7ebe60e2c8300475ae699fc598fa6d1a54e5484b41c38e72d8cf30ae31c430d9"],"state_sha256":"e7979964b991e7d5ab01cdf234339b49a3c05c2a140daedab71759b1c3d3cbd0"}