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Related Experiment Video

Updated: Nov 27, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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From Spin Glasses to Negative-Weight Percolation.

Alexander K Hartmann1, Oliver Melchert2,3, Christoph Norrenbrock1

  • 1Institute of Physics, University of Oldenburg, 26111 Oldenburg, Germany.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces the negative weight percolation (NWP) model for spin glasses, offering a novel algorithmic approach. NWP exhibits distinct universality class properties compared to standard percolation.

Keywords:
disordered systemsfrustrationnegative weight percolationoptimisationphase transition

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Computer Science

Background:

  • Spin glasses are complex random systems modeling magnetic alloys.
  • Investigating spin glass models often involves studying domain walls.
  • Algorithmic analysis in 2D relates domain walls to shortest path calculations with negative weights.

Purpose of the Study:

  • Introduce the negative weight percolation (NWP) model.
  • Provide foundational concepts from spin glasses, graph theory, and algorithms.
  • Summarize a decade of NWP research, including percolation transitions and universality.

Main Methods:

  • Developed the negative weight percolation (NWP) model.
  • Mapped the algorithmic approach to the classical graph matching problem.
  • Analyzed percolation transitions across various dimensions (d=2 to beyond d_u=6) and for random graphs.

Main Results:

  • Demonstrated that NWP belongs to a different universality class than standard percolation.
  • Presented findings on percolation transitions in dimensions up to and beyond the upper critical dimension (d_u=6).
  • Explored NWP properties related to Stochastic-Loewner Evolution and directed NWP.

Conclusions:

  • The negative weight percolation (NWP) model provides a powerful framework for studying spin glasses.
  • NWP exhibits unique characteristics distinct from standard percolation models.
  • Ongoing research continues to explore NWP's properties and applications in different dimensions and graph types.