Freezing into Stripe States in Two-Dimensional Ferromagnets and Crossing Probabilities in Critical Percolation

Abstract

When a two-dimensional Ising ferromagnet is quenched from above the critical temperature to zero temperature, the system eventually converges to either a ground state (all spins aligned) or an infinitely long-lived metastable stripe state. By applying results from percolation theory, we analytically determine the probability to reach the stripe state as a function of the aspect ratio and the form of the boundary conditions. These predictions agree with simulation results. Our approach generally applies to coarsening dynamics of non-conserved scalar fields in two dimensions.

4 pages, 4 figures, 2-column revtex4 format; latest revision fixes small typos in some formulae

References in corpus (5)

• Exact results for curvature-driven coarsening in two dimensions
• Domain growth morphology in curvature driven two dimensional coarsening
• Percolation Crossing Formulas and Conformal Field Theory
• Long term ordering kinetics of the two dimensional q-state Potts model
• On Crossing Event Formulas in Critical Two-Dimensional Percolation

Cited by in corpus (64)

• Scaling behavior of explosive percolation on the square lattice
• Fate of 2D Kinetic Ising Ferromagnets and Critical Percolation Crossing Probabilities
• Curvature-driven coarsening in the two dimensional Potts model
• Topics in coarsening phenomena
• How soon after a zero-temperature quench is the fate of the Ising model sealed?
• Zero-Temperature Relaxation of Three-Dimensional Ising Ferromagnets
• Zero-Temperature Freezing in Three-Dimensional Kinetic Ising Model
• Dynamics of Confident Voting
• Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures
• Critical percolation in the dynamics of the 2d ferromagnetic Ising model
• Frozen into stripes: fate of the critical Ising model after a quench
• Phase ordering percolation and an infinite domain wall in segregating binary Bose-Einstein condensates
• Coarsening and percolation in a disordered ferromagnet
• Spatial evolution of human dialects
• Geometrical properties of Potts model during the coarsening regime
• Opinion Dynamics and Influencing on Random Geometric Graphs
• Slow Cooling of an Ising Ferromagnet
• Defects dynamics following thermal quenches in square spin-ice
• Persistence in the two dimensional ferromagnetic Ising model
• Effective mobility and diffusivity in coarsening processes
• Ageing at the Spin-Glass/Ferromagnet Transition: Monte Carlo Simulation using GPUs
• Zero-Temperature Coarsening in the 2d Potts Model
• Percolation and coarsening in the bidimensional voter model
• Coarsening and percolation in the kinetic $2d$ Ising model with spin exchange updates and the voter model
• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Topology Controlled Potts Coarsening
• Nature vs. Nurture: Predictability in Low-Temperature Ising Dynamics
• Limiting Shapes of Ising Droplets, Ising Fingers, and Ising Solitons
• Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model
• Asymptotic States of Ising Ferromagnets with Long-range Interactions
• Zero temperature coarsening in Ising model with asymmetric second neighbour interaction in two dimensions
• Curvature-driven growth and interfacial noise in the voter model with self-induced zealots
• Thermodynamically Consistent Phase-Field Theory Including Nearest-Neighbor Pair Correlations Explains Failure of Mean-Field Reasoning
• Absorbing states of zero-temperature Glauber dynamics in random networks
• Jamming and metastability in one dimension: from the kinetically constrained Ising chain to the Riviera model
• Fractal character of the phase ordering kinetics of a diluted ferromagnet
• Dynamical cluster size heterogeneity
• Birdsong dialect patterns explained using magnetic domains
• Dynamics of Ising models near zero temperature : Real Space Renormalization Approach
• Equilibrium and non-equilibrium properties of synthetic metamagnetic films: A Monte Carlo study
• Limiting Shapes in Two-Dimensional Ising Ferromagnets
• Long-Time Predictability in Disordered Spin Systems Following a Deep Quench
• Non-equilibrium dynamics in a three state opinion formation model with stochastic extreme switches
• Fate of Ising ferromagnets and antiferromagnets by zero-temperature Glauber dynamics on the two-dimensional Archimedean and 2-uniform lattices
• Statistical Physics of Language Maps in the USA
• Minority spin dynamics in non-homogeneous Ising model: diverging timescales and exponents
• Critical percolation in the ordering kinetics of twisted nematic phases
• Opinion inertia and coarsening in the Persistent Voter model
• Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model
• High-degeneracy Potts coarsening
• Critical clusters in liquid crystals: Fractal geometry and conformal invariance
• Anomalous Ising freezing times
• Norm breaking in a queue -- athermal phase transition
• The dynamics of competitive learning: the role of updates and memory
• Percolation of Domain Walls in the Two-Higgs Doublet Model
• Wrapping probabilities for Potts spin clusters on a torus
• Active-absorbing phase transition and small world behaviour in Ising model on finite addition type networks in two dimensions
• Field-induced freezing in the unfrustrated Ising antiferromagnet
• Zero Temperature Dynamics of Ising Systems on Hypercubes
• Non-equilibrium dynamics in Ising like models with biased initial condition
• Competing with oneself: Introducing self-interaction in a model of competitive learning
• Mixed phases in feedback Ising models
• Dynamic scaling of vorticity in phase-separating superfluid mixtures
• Harnessing finite-size effects to gauge aging in the $2D$ Ising model