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Topology-controlled Potts coarsening.

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This summary is machine-generated.

We discovered unique topological patterns in the kinetic Potts ferromagnet on a triangular lattice after quenching. The system frequently settles into ground states or specific frozen states, with unusual relaxation times observed.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Investigating the long-time relaxation dynamics of magnetic systems is crucial for understanding emergent phenomena.
  • The kinetic Potts model provides a framework for studying phase transitions and coarsening dynamics in magnetic materials.
  • Previous studies have explored Potts model dynamics on various lattices, but triangular lattices present unique geometric constraints.

Purpose of the Study:

  • To uncover and characterize unusual topological features in the kinetic Potts ferromagnet on a triangular lattice.
  • To analyze the relaxation dynamics and final state configurations after quenching to zero temperature.
  • To investigate the scaling behavior of relaxation times and identify novel coarsening features for different Potts states (q).

Main Methods:

  • Simulating the q-state kinetic Potts ferromagnet on a triangular lattice.
  • Applying an instantaneous quench from a zero-magnetization initial state to zero temperature.
  • Analyzing the frequency of different final topological states and measuring relaxation times.

Main Results:

  • For q=3, the system predominantly relaxes to the ground state (≈75%), a frozen three-hexagon state (≈16%), or a two-stripe state (≈9%).
  • Rare topological states, like those with more than three hexagons, occur with very low probabilities (<10^-4).
  • Relaxation to the three-hexagon state exhibits anomalous scaling, with a time proportional to L^2 ln L, where L is the system size.

Conclusions:

  • The triangular lattice induces unusual topological features in the coarsening dynamics of the kinetic Potts ferromagnet.
  • Anomalous scaling of relaxation times suggests unique underlying mechanisms governing the system's approach to equilibrium.
  • The findings provide new insights into Potts model coarsening and topological phenomena on specific lattice structures.