Zero-Temperature Coarsening in the 2d Potts Model

Abstract

We study the fate of the 2d kinetic q-state Potts model after a sudden quench to zero temperature. Both ground states and complicated static states are reached with non-zero probabilities. These outcomes resemble those found in the quench of the 2d Ising model; however, the variety of static states in the q-state Potts model (with q>=3) is much richer than in the Ising model, where static states are either ground or stripe states. Another possibility is that the system gets trapped on a set of equal-energy blinker states where a subset of spins can flip ad infinitum; these states are similar to those found in the quench of the 3d Ising model. The evolution towards the final energy is also unusual---at long times, sudden and massive energy drops may occur that are accompanied by macroscopic reordering of the domain structure. This indeterminacy in the zero-temperature quench of the kinetic Potts model is at odds with basic predictions from the theory of phase-ordering kinetics. We also propose a continuum description of coarsening with more than two equivalent ground states. The resulting time-dependent Ginzburg-Landau equations reproduce the complex cluster patterns that arise in the quench of the kinetic Potts model.

21 pages, 18 figures, 4 movies in supplemental material; version 2: 5 added references and some figures enlarged; version 3: parts of the introduction were rewritten; version 4: a few minor corrections

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Cited by in corpus (10)

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• Topology Controlled Potts Coarsening
• Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model
• How many phases nucleate in the bidimensional Potts model?
• The Tightness of the Kesten-Stigum Reconstruction Bound of Symmetric Model with Multiple Mutations
• Metastability in the Potts model: exact results in the large q limit
• Multinucleation in the first-order phase transition of the 2d Potts model
• High-degeneracy Potts coarsening
• Disentangling Growth and Decay of Domains During Phase Ordering
• Anomalous Ising freezing times