Multi-level approaches to discrete-state and stochastic problems

  • Achi Brandt
  • Dorit Ron
  • Daniel J. Amit
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1228)


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.


Ising Model Coarse Level Single Spin Attraction Basin Spin Glass Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Achi Brandt
    • 1
  • Dorit Ron
    • 1
  • Daniel J. Amit
    • 2
  1. 1.Department of Applied MathematicsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.Racah Institute of PhysicsThe Hebrew UniversityJerusalemIsrael

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