EXACT GROUND-STATES OF ISING SPIN-GLASSES - NEW EXPERIMENTAL RESULTS WITH A BRANCH-AND-CUT ALGORITHM

In this paper we study two-dimensional Ising spin glasses on a grid wi th nearest neighbor and periodic boundary interactions, based on a Gau ssian bond distribution, and an exterior magnetic field. We show how u sing a technique called branch and cut, the exact ground states of gri ds of sizes up to 100 x 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 o n the properties of spin glasses whose errors depend only on the assum ptions on the model and not on the computational process. This feature is a clear advantage of the method over other, more popular ways to c ompute the ground state, like Monte Carlo simulation including simulat ed annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be det ermined a priori. Our ground-state energy estimation at zero field is -1.317.