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02923aam a2200361 i 4500 001 444508A0440211EF98CC15ED37ECA4DB 003 SILO 005 20240717010108 008 240424t20242024fr a f b 000 0 eng d 020 $a 9782856299852 020 $a 2856299857 035 $a (OCoLC)1431124951 040 $a HVC $b eng $e rda $c HVC $d OCLCQ $d CGU $d WTU $d IWA $d SILO 041 1 $a eng $b fre 100 1 $a Dario, Paul $d 1992- $e author. 245 10 $a Massless phases for the villain model in d ⥠3 / $c Paul Dario & Wei Wu. 246 3 $a Massless phases for the villain model in dâ¥3 264 1 $a Paris : $b SocieÌteÌ matheÌmatique de France, $c 2024. 300 $a viii, 217 pages : $b illustrations ; $c 24 cm. 490 1 $a AsteÌrisque, $x 0303-1179 ; $v 447 504 $a Includes bibliographic references (pages 211-217). 505 0 $a Introduction -- Preliminaries -- Duality and Helffer-SjoÌstrand representation -- First-order expansion of the two-point function: overview of the proof -- Regularity theory for low temperature dual Villain model -- Quantitative convergence of the subadditive quantities -- Quantitative homogenization of the Green's matrix -- First-order expansion of the two-point function: technical lemmas -- A. List of notation and preliminary results -- B. Multiscale PoincareÌ inequality -- C. Basic estimates on discrete convolutions. 520 $a "A major open question in statistical mechanics, known as the Gaussian spin wave conjecture, predicts that the low temperature phase of the Abelian spin systems with continuous symmetry behave like Gaussian free fields. In this paper we consider the classical Villain rotator model in Zd, d ⥠3 at sufficiently low temperature, and prove that the truncated two-point function decays asymptotically as SxS2âd, with an algebraic rate of convergence. We also obtain the same asymptotic decay separately for the transversal two-point functions. This quantifies the spontaneous magnetization result for the Villain model at low temperatures and constitutes a first step toward a more precise understanding of the spin-wave conjecture. We believe that our method extends to finite range interactions, and to other Abelian spin systems and Abelian gauge theory in d ⥠3. We also develop a quantitative perspective on homogenization of uniformly convex gradient Gibbs measures"--Abstract. 546 $a In English; abstract also in French. 650 0 $a Spin waves $x Mathematical models. 650 0 $a Mathematical physics. $0 https://id.loc.gov/authorities/subjects/sh85082129 700 1 $a Wu, Wei $c (Mathematician), $e author. 773 18 $w 990002617290102756 $t AsteÌrisque. $g no:v. 447,2024 830 0 $a AsteÌrisque ; $0 https://id.loc.gov/authorities/names/n86716119 $v v. 447. 941 $a 1 952 $l USUX851 $d 20240717023100.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=444508A0440211EF98CC15ED37ECA4DB 994 $a C0 $b IWAInitiate Another SILO Locator Search