{"paper":{"title":"Logarithmic two-point correlators in the Abelian sandpile model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"P. Ruelle, S.Y. Grigorev, V.B. Priezzhev, V.S. Poghosyan","submitted_at":"2010-05-12T13:25:35Z","abstract_excerpt":"We present the detailed calculations of the asymptotics of two-site correlation functions for height variables in the two-dimensional Abelian sandpile model. By using combinatorial methods for the enumeration of spanning trees, we extend the well-known result for the correlation $\\sigma_{1,1} \\simeq 1/r^4$ of minimal heights $h_1=h_2=1$ to $\\sigma_{1,h} = P_{1,h}-P_1P_h$ for height values $h=2,3,4$. These results confirm the dominant logarithmic behaviour $\\sigma_{1,h} \\simeq (c_h\\log r + d_h)/r^4 + {\\cal O}(r^{-5})$ for large $r$, predicted by logarithmic conformal field theory based on field"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2088","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"}