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We develop a method based on functional determinants, equivalent to summing an infinite set of diagrams. We obtain, in dimension d=4-epsilon, the even n-th cumulant of relative displacements as <[u(r)-u(0)]^n>^c = A_n ln r, with A_n = -(\\epsilon/3)^n \\Gamma(n-1/2) \\zeta(2n-3)/\\pi^(1/2), as well as the multifractal dimension x_q of the exponential field e^{q u(r)}. As a corollary, we obtain an analytic expression f"},"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":"1309.6529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-09-25T14:45:30Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"25e3b3cd2281fab4bd9bf8b6a9e0e3aac5c9a823c9a568209cad3e462631f5ce","abstract_canon_sha256":"2b4ee12f0b45561c2a11b7e122238394326a858f12735f07b5bcece20480d831"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:36.976824Z","signature_b64":"ZG+IvFR3FCtdfRAospA7FO2rjCOX9vjgIsamYuzjqh6BBk13JD96cRpWExBRNeOoRDxNqBiPFTSQ89Hp3ji9Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ab43a5dc2b0a0a250c5ddc2668b05a095afb17a932970e8a51ab15d1bbcc9ba","last_reissued_at":"2026-05-18T03:00:36.976066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:36.976066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Gaussian effects and multifractality in the Bragg glass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat.dis-nn","authors_text":"Andrei A. Fedorenko, Kay Joerg Wiese, Pierre Le Doussal","submitted_at":"2013-09-25T14:45:30Z","abstract_excerpt":"We study, beyond the Gaussian approximation, the decay of the translational order correlation function for a d-dimensional scalar periodic elastic system in a disordered environment. We develop a method based on functional determinants, equivalent to summing an infinite set of diagrams. We obtain, in dimension d=4-epsilon, the even n-th cumulant of relative displacements as <[u(r)-u(0)]^n>^c = A_n ln r, with A_n = -(\\epsilon/3)^n \\Gamma(n-1/2) \\zeta(2n-3)/\\pi^(1/2), as well as the multifractal dimension x_q of the exponential field e^{q u(r)}. 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