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Dynamics of an unbounded interface between ordered phases.

P L Krapivsky1, S Redner, J Tailleur

  • 1Center for BioDynamics, Center for Polymer Studies, and Department of Physics, Boston University, Boston, MA 02215, USA. paulk@bu.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2004
PubMed
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The interface in two-dimensional Ising ferromagnets evolves into a self-similar shape. This study analyzes the interface dynamics under zero-temperature Glauber dynamics, revealing its limiting form.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Two-dimensional Ising ferromagnets exhibit ordered phases.
  • Interfaces between these phases are crucial for understanding domain structures.
  • Zero-temperature Glauber dynamics provide a simplified model for interface evolution.

Purpose of the Study:

  • To investigate the evolution of an unbounded interface in 2D Ising ferromagnets.
  • To analyze interface dynamics with initial configurations of one or two corners.
  • To determine the limiting self-similar form of the evolving interface.

Main Methods:

  • Simulating single-spin-flip zero-temperature Glauber dynamics.
  • Applying the continuum time-dependent Ginzburg-Landau equation.
  • Utilizing a microscopic approach to calculate interface shape.

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Main Results:

  • The interface consistently evolves to a limiting self-similar form.
  • Both one- and two-corner initial configurations lead to this self-similar state.
  • A correspondence was found between the single-corner interface and integer partitions (Young diagrams).

Conclusions:

  • The interface dynamics in this system are predictable and tend towards a universal self-similar state.
  • The study provides both continuum and microscopic insights into interface evolution.
  • The connection to Young diagrams offers a novel mathematical perspective on physical interfaces.