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Critical slowing down in polynomial time algorithms.

A Alan Middleton1

  • 1Department of Physics, Syracuse University, Syracuse, NY 13244, USA.

Physical Review Letters
|January 22, 2002
PubMed
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Exact ground state computations for disordered magnets slow down at zero temperature phase transitions. Algorithm operations for spin glasses and Ising models were estimated using physical properties, potentially speeding up computations.

Area of Science:

  • Physics
  • Computer Science
  • Materials Science

Background:

  • Combinatorial optimization algorithms are crucial for determining ground states in disordered magnetic systems.
  • These algorithms exhibit critical slowing down near zero-temperature phase transitions, impacting computational efficiency.

Purpose of the Study:

  • To estimate the number of operations for specific algorithms (push-relabel and 2D spin glass) in disordered magnets.
  • To connect algorithmic performance with the physical characteristics of magnetic models.

Main Methods:

  • Utilizing physical features like vanishing stiffness and ground state degeneracy.
  • Estimating computational complexity for the push-relabel algorithm applied to the random field Ising model.
  • Analyzing the algorithm for the 2D spin glass model.

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Main Results:

  • The number of operations for the analyzed algorithms was estimated based on physical model properties.
  • A clear link was established between the physical behavior of disordered magnets and algorithmic performance.
  • Insights into computational bottlenecks at phase transitions were gained.

Conclusions:

  • The study strengthens the relationship between computational algorithms and physical models of disordered magnets.
  • Understanding these connections can lead to improved computational speeds for ground state calculations.
  • This research offers a pathway for optimizing algorithms in condensed matter physics and materials science.