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Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope
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Limiting shapes in two-dimensional Ising ferromagnets.

P L Krapivsky1, Jason Olejarz

  • 1Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 16, 2013
PubMed
Summary
This summary is machine-generated.

We studied the Ising model with long-range interactions and found that interfaces evolve diffusively. The study determines the limiting shapes and dynamics for receding interfaces and translating "fingers".

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • The Ising model is a fundamental model in statistical mechanics.
  • Interactions beyond nearest neighbors significantly alter model behavior.
  • Understanding interface dynamics is crucial for phase transitions.

Purpose of the Study:

  • Investigate the zero-temperature interface evolution in a 2D Ising model.
  • Analyze the impact of ferromagnetic interactions beyond nearest neighbors.
  • Determine the limiting shapes and dynamics of evolving interfaces.

Main Methods:

  • Simulations of the Ising model on a square lattice.
  • Analysis of zero-temperature spin-flip dynamics.
  • Analytical calculations and numerical verification of interface shapes.

Main Results:

  • Interfaces recede in a self-similar, diffusive manner for quadrant boundaries.
  • A deterministic limiting shape for receding interfaces was determined analytically.
  • Semi-infinite bars form stationary, finger-like shapes that translate axially.

Conclusions:

  • The study provides analytical and numerical insights into non-trivial interface dynamics.
  • The Ising model with extended interactions exhibits complex emergent behavior.
  • Predictions for limiting shapes and velocities of evolving interfaces are established.