Abstract
Fast multi-level techniques are developed for large-scale problems whose variables may assume only discrete values (such as spins with only “up” and “down” states), and/or where the relations between variables is probabilistic. Motivation and examples are taken from statistical mechanics and field theory. Detailed procedures are developed for the fast global minimization of discretestate functionals, or other functionals with many local minima, using new principles of multilevel interactions. Tests with Ising spin models are reported. Of special interest to physicists are the Ising model in a random field and spin glasses, which are known to lead to difficulties in conventional Monte-Carlo algorithms.
Research supported by the Air Force Aeronautical Laboratories, Air Force Systems Command, United States Air force, under Grant AFOSR 84-0070.
Research supported in part by the Fund of Basic Research of the Israel Academy of Science and Humanities.
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Brandt, A., Ron, D., Amit, D.J. (1986). Multi-level approaches to discrete-state and stochastic problems. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods II. Lecture Notes in Mathematics, vol 1228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072642
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DOI: https://doi.org/10.1007/BFb0072642
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