Multi-level approaches to discrete-state and stochastic problems
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.
KeywordsIsing Model Coarse Level Single Spin Attraction Basin Spin Glass Model
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- J.C. Angles D'Auriac and R. Rammal: Phase Diagram of the Random Field Ising Model. CNR Grenoble, preprint, 1986.Google Scholar
- A. Brandt: Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics. Monograph, 191 pages. Available as GMD Studien 85 from GMD-AIW, Postfach 1240, D-5205, St. Augustin 1, W. Germany.Google Scholar
- R. Graham and F. Haake: Quantum Statistics in Optics and Solid-State Physics. Springer Tracts in Modern Physics, Vol. 66, Springer-Verlag, Berlin, 1973.Google Scholar
- A. Hasenfratz and P. Hasenfratz: Lattice Gauge Theories. Florida State University, preprint FSU-SCRI 85-2, 1985.Google Scholar
- S. Kirkpatrick: Models of disordered systems. Lecture Notes in Physics 149 (C. Castellani et al., eds.), Springer-Verlag, Berlin, 280.Google Scholar
- N.D. Mackenzie and A.P. Young: Statics and dynamics of the infinite range Ising spin glass model. J. Phys. C16 (1983), 5321.Google Scholar
- R.L. Stratonovich: Topics in the Theory of Random Noise, Vol. 1, Gordon and Breach, New York, 1963.Google Scholar