MPI-I-96-1-004

In this paper we study the problem of finding an exact ground state of a two-dimensional $\pm J$ Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is a concentration $p$ of negative bonds, with $p$ ranging between $0.1$ and $0.9$. With our exact algorithm we can determine ground states of grids of sizes up to $50\times 50$ in a moderate amount of computation time (up to one hour each) for several values of $p$. For the ground state energy of an infinite spin glass system with $p=0.5$ we estimate $E_{0.5}^\infty = -1.4015 \pm0.0008$. We report on extensive computational tests based on more than $22\,000$ experiments.