Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model
arXiv:1709.05268 · doi:10.1088/1742-5468/aa9bb4
Abstract
We show that the equilibrium interfaces in the disordered phase have critical percolation fractal dimension over a wide range of length scales. We confirm that the system falls out of equilibrium at a temperature that depends on the cooling rate as predicted by the Kibble-Zurek argument and we prove that the dynamic growing length once the cooling reaches the critical point satisfies the same scaling. We determine the dynamic scaling properties of the interface winding angle variance and we show that the crossover between critical Ising and critical percolation properties is determined by the growing length reached when the system fell out of equilibrium.
18 pages, 6 figures
References in corpus (17)
- Recent advances in percolation theory and its applications
- Critical Dynamics of Spontaneous Symmetry Breaking in a Homogeneous Bose gas
- Emergence of coherence in a uniform quasi-two-dimensional Bose gas
- Structural defects in ion crystals by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism
- Exact results for curvature-driven coarsening in two dimensions
- Domain growth morphology in curvature driven two dimensional coarsening
- Exploring the Kibble-Zurek mechanism with homogeneous Bose gases
- Winding angle variance of Fortuin-Kasteleyn contours
- Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark
- Zero-Temperature Relaxation of Three-Dimensional Ising Ferromagnets
- Zero-Temperature Freezing in Three-Dimensional Kinetic Ising Model
- Geometric properties of two-dimensional coarsening with weak disorder
- Thermal Behavior of Spin Clusters and Interfaces in two-dimensional Ising Model on Square Lattice
- Fields, particles and universality in two dimensions
- Coarsening and percolation in a disordered ferromagnet
- Dynamic scaling in the 2D Ising spin glass with Gaussian couplings
- Phase separation and critical percolation in bidimensional spin-exchange models
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