Wishart planted ensemble: A tunably rugged pairwise Ising model with a first-order phase transition.

@article{Hamze2020WishartPE,
  title={Wishart planted ensemble: A tunably rugged pairwise Ising model with a first-order phase transition.},
  author={Firas Hamze and Jack Raymond and Christopher Pattison and Katja Biswas and Helmut G. Katzgraber},
  journal={Physical review. E},
  year={2020},
  volume={101 5-1},
  pages={
          052102
        }
}
We propose the Wishart planted ensemble, a class of zero-field Ising models with tunable algorithmic hardness and specifiable (or planted) ground state. The problem class arises from a simple procedure for generating a family of random integer programming problems with specific statistical symmetry properties but turns out to have intimate connections to a sign-inverted variant of the Hopfield model. The Hamiltonian contains only 2-spin interactions, with the coupler matrix following a type of… 
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