# 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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## References

SHOWING 1-10 OF 104 REFERENCES

Mean-field equations for spin models with orthogonal interaction matrices

- Physics, Mathematics
- 1995

We study the metastable states in Ising spin models with orthogonal interaction matrices. We focus on three realizations of this model, the random case and two non-random cases, i.e. the…

Finding Low-Temperature States With Parallel Tempering, Simulated Annealing And Simple Monte Carlo

- Physics
- 2002

Monte Carlo simulation techniques, like simulated annealing and parallel tempering, are often used to evaluate low-temperature properties and find ground states of disordered systems. Here we compare…

Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution

- Physics
- 1993

We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicLd geometry,L being the linear dimension of the system, and surface effects are avoided by periodic…

From near to eternity: Spin-glass planting, tiling puzzles, and constraint-satisfaction problems.

- Mathematics, MedicinePhysical review. E
- 2018

By varying the proportions of subproblem types, the Hamiltonian can span a dramatic range of typical computational complexity, from fairly easy to many orders of magnitude more difficult than prototypical bimodal and Gaussian spin glasses in three space dimensions.

MONTE CARLO METHODS FOR FIRST ORDER PHASE TRANSITIONS: SOME RECENT PROGRESS

- Mathematics
- 1992

This brief review discusses methods to locate and characterize first order phase transitions, paying particular attention to finite size effects. In the first part, the order parameter probability…

Weighted averages and order parameters for the infinite range Ising spin glass

- Physics
- 1983

The Sherrington-Kirkpatrick spin glass model (1975) is studied by replicas and by analysing the mean field equations of Thouless, Anderson and Palmer (TAP) (1977). The authors show that the standard…

Probing for quantum speedup in spin-glass problems with planted solutions

- Physics
- 2015

The availability of quantum annealing devices with hundreds of qubits has made the experimental demonstration of a quantum speedup for optimization problems a coveted, albeit elusive goal. Going…

Spin-glass models of neural networks.

- Physics, MedicinePhysical review. A, General physics
- 1985

Two dynamical models, proposed by Hopfield and Little to account for the collective behavior of neural networks, are analyzed and it is shown that the long-time behavior of the two models is identical, for all temperatures below a transition temperature ${T}_{c}$.

Mean-field theory for a spin-glass model of neural networks: TAP free energy and the paramagnetic to spin-glass transition

- Physics
- 1997

An approach is proposed to the Hopfield model where the mean-field treatment is made for a given set of stored patterns (sample) and then the statistical average over samples is taken. This…

SPIN GLASS STATES OF THE ANTI-HOPFIELD MODEL

- Physics
- 1998

We study the Hopfield model with an opposite interactional sign by using a one-step replica symmetry breaking ansatz and the marginality condition. We show that this model belongs to spin glass…