An algorithm is presented which finds a surprisingly good approximation to the global minimum of a not necessarily convex, quadratic function in N variables, restricted to a N-dimensional cube. For instance, all Ising Hamiltonians with pair interactions belong to this class. In general, the time complexity of the algorithm is O(N4). For nearest-neighbour interactions, it reduces to O(N3). The algorithm is used to find the ground state of various Ising spin glass models and to study the zero-temperature behaviour of the magnetization as a function of the external field h in both two and three dimensions. It is found that the two-dimensional ± J model has a nonzero magnetization as h → 0.
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Canisius et al. (1986) studied this question.
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