Exact ground states of two-dimensional +/-J ising spin glasses

In this paper we study the problem of finding an exact ground state of a two-dimensional +/-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 x 50 in a moderate amount of computation time (up to 1 hr 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)(infinity) = -1.4015 +/- 0.0008. We report on extensive computational tests based on more than 22,000 experiments.