Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT

@article{Huang2016FindingAP,
  title={Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT},
  author={Wenxuan Huang and Daniil A. Kitchaev and Stephen T. Dacek and Ziqin Rong and Alexander Urban and Shan Cao and Chuan Luo and Gerbrand Ceder},
  journal={Physical Review B},
  year={2016},
  volume={94},
  pages={134424}
}
This paper was supported primarily by the US Department of Energy (DOE) under Contract No. DE-FG02-96ER45571. In addition, some of the test cases for ground states were supported by the Office of Naval Research under contract N00014-14-1-0444. 

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References

SHOWING 1-10 OF 74 REFERENCES

A Method of Determining the Ground State of the Extended-Range Classical Lattice Gas Model

A method of deriving geometrical inequalities by the use of which the ground state of the extended-range classica:l lattice gas model can be analytically determined is developed. As illustrative

Pseudo-Boolean optimization

CCLS: An Efficient Local Search Algorithm for Weighted Maximum Satisfiability

Experimental results illustrate that the quality of solution found by CCLS is much better than that found by IRoTS, akmaxsat_ls and New WPM2 on most industrial, crafted and random instances, indicating the efficiency and the robustness of the CCRS algorithm.

The First and Second Max-SAT Evaluations

The main objectives of both evaluations were assessing the advancements in the field of Max-SAT solvers through a comparison of their performances, identifying successful solving techniques and encouraging researchers to develop new ones, and creating a publicly available collection of challenging Max- SAT benchmarks.

Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields

A quantum gas trapped in an optical lattice of triangular symmetry can now be driven from a paramagnetic to an antiferromagnetic state by a tunable artificial magnetic field.

Satisfiability Solvers

The efficiency of subgradient projection methods for convex optimization, part I: general level methods

Subgradient methods for convex optimization that use projections onto successive approximations of level sets of the objective corresponding to estimates of the optimal value enjoy almost optimal efficiency estimates.
...