# 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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