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- Title
Ising Model with Curie–Weiss Perturbation.
- Authors
Camia, Federico; Jiang, Jianping; Newman, Charles M.
- Abstract
Consider the nearest-neighbor Ising model on Λ n : = [ - n , n ] d ∩ Z d at inverse temperature β ≥ 0 with free boundary conditions, and let Y n (σ) : = ∑ u ∈ Λ n σ u be its total magnetization. Let X n be the total magnetization perturbed by a critical Curie–Weiss interaction, i.e., d F X n d F Y n (x) : = exp [ x 2 / 2 ⟨ Y n 2 ⟩ Λ n , β ] exp [ Y n 2 / 2 ⟨ Y n 2 ⟩ Λ n , β ] Λ n , β , <graphic href="10955_2022_2935_Article_Equ156.gif"></graphic> where F X n and F Y n are the distribution functions for X n and Y n respectively. We prove that for any d ≥ 4 and β ∈ [ 0 , β c (d) ] where β c (d) is the critical inverse temperature, any subsequential limit (in distribution) of { X n / E X n 2 : n ∈ N } has an analytic density (say, f X ) all of whose zeros are pure imaginary, and f X has an explicit expression in terms of the asymptotic behavior of zeros for the moment generating function of Y n . We also prove that for any d ≥ 1 and then for β small, f X (x) = K exp (- C 4 x 4) , <graphic href="10955_2022_2935_Article_Equ157.gif"></graphic> where C = Γ (3 / 4) / Γ (1 / 4) and K = Γ (3 / 4) / (4 Γ (5 / 4) 3 / 2) . Possible connections between f X and the high-dimensional critical Ising model with periodic boundary conditions are discussed.
- Publication
Journal of Statistical Physics, 2022, Vol 188, Issue 1, p1
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-022-02935-1