On the Two-Point Function of the Ising Model with Infinite-Range Interactions

Article Article scientifique Article On the Two-Point Function of the Ising Model with Infinite-Range Interactions eng 2023-10-26 2023-10-26 author Aoun Yacine 0009-0008-3096-0746 834518 Section de mathématiques (MATH) author Khettabi Kamil 864310 Section de mathématiques (MATH) 1-19 168 10.1007/s10955-023-03175-7 0022-4715 https://link.springer.com/10.1007/s10955-023-03175-7 In this article, we prove some results concerning the truncated two-point function of the infinite-range Ising model above and below the critical temperature. More precisely, if the coupling constants are of the form Jx = ψ(x)e-ρ(x) with ρ some norm and ψ an subexponential correction, we show under appropriate assumptions that given s ∈ Sd-1, the Laplace transform of the two-point function in the direction s is infinite for β = βsat(s) (where βsat(s) is a the biggest value such that the inverse correlation length νβ(s) associated to the truncated two-point function is equal to ρ(s) on [0, βsat(s))). Moreover, we prove that the two-point function satisfies up-to-constants Ornstein-Zernike asymptotics for β = βsat(s) on Z. As far as we know, this constitutes the first result on the behaviour of the two-point function at βsat(s). Finally, we show that there exists β0 such that for every β > β0, νβ(s) = ρ(s). All the results are new and their proofs are built on different results and ideas developed in Duminil-Copin and Tassion (Commun Math Phys 359(2):821–822, 2018) and Aoun et al. in (Commun Math Phys 386:433–467, 2021). Ising model Percolation FK percolation Ornstein-Zernike asymptotics Ornstein-Zernike Saturation transition Dewey 510 Swiss National Science Foundation Sharp asymptotics of correlations in lattice systems 200422 CH Projects 25 Section de mathématiques 11 false Journal of statistical physics 190 11 ac47dada-a4c2-46f9-9ffe-bf43620f4db5 Article (Published version) Public Article_scientifique_from_unpaywall.pdf 435546 application/pdf CC BY-4.0 9c408320081c21b1b4ecb03190a58722cdd0bfc1a7ef6a82968295173e98afba openAccess Faculté des sciences / Section de mathématiques

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On the Two-Point Function of the Ising Model with Infinite-Range Interactions	Journal of statistical physics			2023	22	15

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Khettabi, Kamil