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Exact ground states of Ising spin classes: new experimental results with a branch and cut algorithm

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Mutzel,  Petra
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-95-1-004.pdf
(Any fulltext), 130KB

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Citation

Diehl, M., De Simone, C., Jünger, M., Mutzel, P., Reinelt, G., & Rinaldi, G.(1995). Exact ground states of Ising spin classes: new experimental results with a branch and cut algorithm (MPI-I-1995-1-004). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-A765-7
Abstract
In this paper we study 2-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to $100\times 100$ can be determined in a moderate amount of computation time, and we report on extensive computational tests. With our method we produce results based on more than $20\,000$ experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other more popular ways to compute the ground state, like Monte Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determined a priori. Our ground state energy estimation at zero field is~$-1.317$.