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}
}
. 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… 

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