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Abstract: A sampling algorithm is presented that generates spin glass configurations ofthe 2D Edwards-Anderson Ising spin glass at finite temperature, withprobabilities proportional to their Boltzmann weights. Such an algorithmovercomes the slow dynamics of direct simulation and can be used to studylong-range correlation functions and coarse-grained dynamics. The algorithmuses a correspondence between spin configurations on a regular lattice anddimer edge coverings of a related graph: Wilson-s algorithm D. B. Wilson,Proc. 8th Symp. Discrete Algorithms 258, 1997 for sampling dimer coveringson a planar lattice is adapted to generate samplings for the dimer problemcorresponding to both planar and toroidal spin glass samples. This algorithm isrecursive: it computes probabilities for spins along a -separator- that dividesthe sample in half. Given the spins on the separator, sample configurations forthe two separated halves are generated by further division and assignment. Thealgorithm is simplified by using Pfaffian elimination, rather than Gaussianelimination, for sampling dimer configurations. For n spins and given floatingpoint precision, the algorithm has an asymptotic run-time of On^{3-2}; it isfound that the required precision scales as inverse temperature and grows onlyslowly with system size. Sample applications and benchmarking results arepresented for samples of size up to n=128^2, with fixed and periodic boundaryconditions.



Autor: Creighton K. Thomas, A. Alan Middleton

Fuente: https://arxiv.org/







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