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We describe an exact integer algorithm to compute the partition function of a two-dimensional plus or minus J Ising spin glass. Given a set of quenched random bonds, the algorithm returns the density of states as a function of energy. The computation time is polynomial in the lattice size. We investigate defects, low-lying excitations, and zeros of the partition function in the complex plane. We also discuss the potential to examine other types of quenched randomness.
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