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Zero-temperature relaxation of three-dimensional Ising ferromagnets
J Olejarz1, P L Krapivsky, S Redner
1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
The Ising-Glauber model exhibits extremely slow relaxation at zero temperature, with system size impacting characteristic time scales exponentially. Many systems feature "blinker" spins, causing perpetual wandering through complex, multi-holed domain states.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- The Ising-Glauber model is a fundamental tool for studying magnetic systems.
- Understanding system dynamics after a rapid temperature change (quench) is crucial.
Purpose of the Study:
- Investigate the properties of the Ising-Glauber model on a periodic cubic lattice after a quench to zero temperature.
- Characterize the slow relaxation dynamics and long-time behavior.
Main Methods:
- Numerical simulations on a periodic cubic lattice.
- Heuristic analysis of system evolution and spin-flip events.
Main Results:
- Extremely slow relaxation observed, characterized by wandering on constant energy plateaus.
- Characteristic relaxation time scale τ grows exponentially with system size L, τ~exp(L^2).
- Long-time states feature persistent "blinker" spins, leading to infinite wandering through equal-energy states.
Conclusions:
- The Ising-Glauber model at zero temperature exhibits complex, non-static long-time behavior.
- Topologically complex domains with high genus (scaling as L^1.7) characterize the blinker states.
- The system dynamics are dominated by the emergent "plumber's nightmare" geometry of interwoven domains.
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