Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model

Abstract

After a sudden quench from the disordered high-temperature $T_0\to \infty$ phase to a final temperature below the critical point $T_F\ll T_c$, the non-conserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice (2dIM) initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time $t_{{\mathrm{p}}_1}>0$) and stabilization (at time $t_{\mathrm{p}}>t_{{\mathrm{p}}_1}$) of a giant percolation cluster, as previously reported. However, the microscopic mechanisms that control such timescales are not yet fully understood. In this paper, in order to study their role on each time regime after the quench ($T_F=0$), we distinguish between spin flips that decrease the total energy of the system from those that keep it constant, the latter being parametrized by the probability $p$. We show that the cluster size heterogeneity $H(t,p)$ and the typical domain size $\ell (t,p)$ have no dependence on $p$ in the first time regime up to $t_{{\mathrm{p}}_1}$. On the other hand, the time for stabilizing a percolating cluster is controlled by the acceptance probability of constant-energy flips: $t_{\mathrm{p}}(p)\sim p^{-1}$ for $p\ll 1$ (at $p=0$, the dynamics gets stuck in a metastable state). These flips are also the relevant ones in the later coarsening regime where dynamical scaling takes place. Because the phenomenology on the approach to the percolation point seems to be shared by many 2d systems with a non-conserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and effective way to set, through the dynamics itself, $t_{{\mathrm{p}}_1}$ and $t_{\mathrm{p}}$ in such systems.

arXiv comment7 pages, 4 figures; supplemental material: 1 video

References in corpus (33)

• Theory of Phase Ordering Kinetics
• Colloidal Gels: Equilibrium and Non-Equilibrium Routes
• Coarsening and persistence in the voter model
• Fate of Zero-Temperature Ising Ferromagnets
• Freezing in Ising Ferromagnets
• Freezing into Stripe States in Two-Dimensional Ferromagnets and Crossing Probabilities in Critical Percolation
• Exact results for curvature-driven coarsening in two dimensions
• Continuity of the Explosive Percolation Transition
• Domain growth morphology in curvature driven two dimensional coarsening
• Fate of 2D Kinetic Ising Ferromagnets and Critical Percolation Crossing Probabilities
• Curvature-driven coarsening in the two dimensional Potts model
• Geometry of phase separation
• How soon after a zero-temperature quench is the fate of the Ising model sealed?
• Tapping Thermodynamics of the One Dimensional Ising Model
• Zero-Temperature Relaxation of Three-Dimensional Ising Ferromagnets
• Experimental test of curvature-driven dynamics in the phase ordering of a two dimensional liquid crystal
• Metastability in zero-temperature dynamics: Statistics of attractors
• Critical percolation in the dynamics of the 2d ferromagnetic Ising model
• Geometrical properties of Potts model during the coarsening regime
• Maximal Diversity and Zipf's Law
• Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals
• Percolation and coarsening in the bidimensional voter model
• Scaling of cluster heterogeneity in percolation transitions
• Coarsening and percolation in the kinetic $2d$ Ising model with spin exchange updates and the voter model
• Topology Controlled Potts Coarsening
• Analytical solution of a one-dimensional Ising model with zero temperature dynamics
• Cluster-size heterogeneity in the two-dimensional Ising model
• Curvature-driven growth and interfacial noise in the voter model with self-induced zealots
• Phase separation and critical percolation in bidimensional spin-exchange models
• Dynamical cluster size heterogeneity
• Low-temperature universal dynamics of the bidimensional Potts model in the large q limit
• Domain size heterogeneity in the Ising model: geometrical and thermal transitions
• A branching random-walk model of disease outbreaks and the percolation backbone

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