• DOI:10.1007/s10955-022-02935-1
• Corpus ID: 243860934

Ising Model with Curie–Weiss Perturbation

@article{Camia2022IsingMW,
  title={Ising Model with Curie–Weiss Perturbation},
  author={Federico Camia and Jianping Jiang and Charles M. Newman},
  journal={Journal of Statistical Physics},
  year={2022}
}

• F. Camia, Jianping Jiang, C. Newman
• Published 9 November 2021
• Mathematics
• Journal of Statistical Physics

. 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 ) := P 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., 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 / p E ( X 2 n : 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, where C = p Γ(3 / 4) / Γ(1 / 4) and K = p ). Possible connections between f X and the high-dimensional critical Ising model with periodic boundary conditions are discussed.