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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~$-1.317$.
