Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model

Ricateau, Hugo; Cugliandolo, Leticia F.; Picco, Marco

doi:10.1088/1742-5468/aa9bb4

Cited by 16 publications

(17 citation statements)

References 67 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The best scaling is achieved by using D A 1.93 and D 1.53 for the largest cluster size and the length of its hull, respectively, and z p 1. 67. We confirm what is found for the scaling of the wrapping probabilities, that is the existence of a time scale t p (L) ∼ L zp that marks the end of a first scaling regime and the entrance into the last coarsening one.…”

Section: Largest Cluster Scalingsupporting

confidence: 87%

Coarsening and percolation in the kinetic 2d Ising model with spin exchange updates and the voter model

Tartaglia¹,

Cugliandolo²,

Picco³

2018

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

We study the early time dynamics of bimodal spin systems on 2d lattices evolving with different microscopic stochastic updates. We treat the ferromagnetic Ising model with locally conserved order parameter (Kawasaki dynamics), the same model with globally conserved order parameter (nonlocal spin exchanges), and the voter model. As already observed for non-conserved order parameter dynamics (Glauber dynamics), in all the cases in which the stochastic dynamics satisfy detailed balance, the critical percolation state persists over a long period of time before usual coarsening of domains takes over and eventually takes the system to equilibrium. By studying the geometrical and statistical properties of time-evolving spin clusters we are able to identify a characteristic length p (t), different from the usual length d (t) ∼ t 1/z d that describes the late time coarsening, that is involved in all scaling relations in the approach to the critical percolation regime. We find that this characteristic length depends on the particular microscopic dynamics and the lattice geometry. In the case of the voter model, we observe that the system briefly passes through a critical percolation state, to later approach a dynamical regime in which the scaling behaviour of the geometrical properties of the ordered domains can be ascribed to a different criticality.arXiv:1805.05775v2 [cond-mat.stat-mech]

show abstract

Section: Largest Cluster Scalingsupporting

confidence: 87%

Coarsening and percolation in the kinetic 2d Ising model with spin exchange updates and the voter model

Tartaglia¹,

Cugliandolo²,

Picco³

2018

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Given that the two processes contribute additively to the overall rate in Eq. (22) we expect a > 0. Analogously, for the 3D star model, the improved scaling argument should take the form…”

Section: B Combining Evaporation and Annihilationmentioning

confidence: 80%

Dynamic scaling of topological ordering in classical systems

Castelnovo

Melko

et al. 2018

Phys. Rev. B

View full text Add to dashboard Cite

We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional Z2 (Ising) lattice gauge model, which exhibits a continuous topological phase transition at finite temperature. We show that a generalized Kibble-Zurek scaling ansatz applies to this transition, in spite of the absence of a local order parameter. We find perimeter-law scaling of the magnitude of a non-local order parameter (defined using Wilson loops) and a dynamic exponent z = 2.70 ± 0.03, the latter in good agreement with previous results for the equilibrium dynamics (autocorrelations). We then study systems where (topological) order forms only at zero temperature-the Ising chain, the two-dimensional Z2 gauge model, and a threedimensional star model (another variant of the Z2 gauge model). In these systems the correlation length diverges exponentially, in a way that is non-smooth as a finite-size system approaches the zero temperature state. We show that the Kibble-Zurek theory does not apply in any of these systems. Instead, the dynamics can be understood in terms of diffusion and annihilation of topological defects, which we use to formulate a scaling theory in good agreement with our simulation results. We also discuss the effect of open boundaries where defect annihilation competes with a faster process of evaporation at the surface.

show abstract

“…In the presence of these competing mechanisms, one expects a peak in H eq . Remarkably, for geometric domains, two peaks are present [15], one near the temperature where the percolating cluster first appears [31] and a second one very close to T c . We here extended this equilibrium measure of how heterogeneous the domains are in size, to non-equilibrium situations, H(t).…”

Section: Discussionmentioning

confidence: 99%

Dynamical cluster size heterogeneity

et al. 2020

View full text Add to dashboard Cite

Only recently the essential role of the percolation critical point has been considered on the dynamical properties of connected regions of aligned spins (domains) after a sudden temperature quench. In equilibrium, it is possible to resolve the contribution to criticality by the thermal and percolative effects (on finite lattices, while in the thermodynamic limit they merge at a single critical temperature) by studying the cluster size heterogeneity, Heq(T ), a measure of how different the domains are in size. We here extend this equilibrium measure and study its temporal evolution, H(t), after driving the system out of equilibrium by a sudden quench in temperature. We show that this single parameter is able to detect and well separate the different time regimes, related to the two time scales in the problem, the short, percolative and the long, coarsening one.

show abstract

Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model

Cited by 16 publications

References 67 publications

Coarsening and percolation in the kinetic 2d Ising model with spin exchange updates and the voter model

Coarsening and percolation in the kinetic 2d Ising model with spin exchange updates and the voter model

Dynamic scaling of topological ordering in classical systems

Dynamical cluster size heterogeneity

Contact Info

Product

Resources

About