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Related Experiment Videos

Phase transition versus disorder: A criterion derived from a two-dimensional dynamic ferromagnetic model.

E W Montroll1, H Reiss

  • 1Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742.

Proceedings of the National Academy of Sciences of the United States of America
|May 1, 1981
PubMed
Summary

Rapidly cooling the two-dimensional Ising model can prevent spin ordering. Under specific hyperbolic cooling, the system freezes into a disordered state due to insufficient time for ordering effects to manifest.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics

Background:

  • The two-dimensional Ising model describes magnetic materials.
  • Understanding spin dynamics under rapid temperature changes is crucial.

Purpose of the Study:

  • To investigate spin correlation functions in a 2D Ising model under rapid cooling.
  • To analyze the impact of hyperbolic cooling on system ordering.

Main Methods:

  • Solving dynamical equations for spin correlation functions.
  • Applying a hyperbolic cooling schedule: T(-1) = T(0) (-1) + bt.
  • Analyzing the system's behavior for large cooling constants (b).

Main Results:

  • For large b, the ordering term in dynamical equations becomes ineffective.

Related Experiment Videos

  • The system freezes into a disordered state during rapid quenches.
  • Correlation length is determined by random walker diffusion distance during cooling.

    • Conclusions:

    • Rapid hyperbolic cooling can suppress order in the 2D Ising model.
    • The rate of cooling significantly impacts the final state of the system.
    • The correlation length provides a measure of disorder in quenched systems.