Cluster–Exact Approximation of Spin Glass Groundstates

We present an algorithm which calculates groundstates of Ising spin glasses approximately. It works by randomly selecting clusters of spins which exhibit no frustrations. The spins which were not selected, contribute to the local fields of the selected spins. For the spin–cluster a groundstate is exactly calaculated by using graphtheoretical methods. The other spins remain unchanged. This procedure is repeated many times resulting in a state with low energy. The total time complexity of this scheme is approximately cubic. We estimate that the groundstate energy density of the infinite system for the ±J model is −1.400± 0.005 (2d) and −1.766 ± 0.002 (3d). The distribution of overlaps for selected systems is calculated in order to characterize the algorithm. The combination of frustration and randomness makes it difficult to find groundstates of spin glasses [1] using numerical simulations. In the past years many methods [2] have been proposed including the multicanonical ensemble [3], genetic algorithms [4], a scheme, which uses storing of spin configurations [5], and an exact algorithm exhibiting exponential timecomplexity [6]. In this paper ∗e-mail: [email protected]