How soon after a zero-temperature quench is the fate of the Ising model sealed?

Blanchard, Thibault; Corberi, Federico; Cugliandolo, Leticia F.; Picco, Marco

doi:10.1209/0295-5075/106/66001

Cited by 47 publications

(113 citation statements)

References 25 publications

(56 reference statements)

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“…We anticipate that we found a small change in the dependence of z p on n c and z d with respect to the one given in Eq. (1.2) [13]. In order to give strong support to our statements we show results for quantities that have not been considered in previous works and we set the stage for the discussion of other microscopic dynamics that we will treat in a future publication.…”

Section: Introductionsupporting

confidence: 59%

“…and it was used in [13] to estimate t p (L), the time after which the percolating structure no longer changes, in the Ising model with kinetic Monte Carlo dynamics with non-conserved order parameter. We will not spend much time discussing persistence, but we will just measure the exponent that characterises its decay in time to refute claims in the literature for its identity with the one of the vanishing waiting time overlap, Q(t, 0; L).…”

Section: Observablesmentioning

confidence: 99%

“…Numerically, an algebraic dependence was found [13] t p L zp (1.1) with an exponent z p that depends on the coordination of the lattice, n c , and the microscopic dynamics. In [13] the following conjecture on its dependence on n c and the conventional dynamic exponent, z d = 2,…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Critical percolation in the dynamics of the 2D ferromagnetic Ising model

Blanchard¹,

Cugliandolo²,

Picco³

et al. 2017

J. Stat. Mech.

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Abstract. We study the early time dynamics of the 2d ferromagnetic Ising model instantaneously quenched from the disordered to the ordered, low temperature, phase. We evolve the system with kinetic Monte Carlo rules that do not conserve the order parameter. We confirm the rapid approach to random critical percolation in a time-scale that diverges with the system size but is much shorter than the equilibration time. We study the scaling properties of the evolution towards critical percolation and we identify an associated growing length, different from the curvature driven one. By working with the model defined on square, triangular and honeycomb microscopic geometries we establish the dependence of this growing length on the lattice coordination. We discuss the interplay with the usual coarsening mechanism and the eventual fall into and escape from metastability.arXiv:1705.06508v3 [cond-mat.stat-mech]

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Section: Introductionsupporting

confidence: 59%

Section: Observablesmentioning

confidence: 99%

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Critical percolation in the dynamics of the 2D ferromagnetic Ising model

Blanchard¹,

Cugliandolo²,

Picco³

et al. 2017

J. Stat. Mech.

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show abstract

“…This result shows that the autocorrelation function takes the general scaling form of Eq. (13) and that…”

Section: Observablesmentioning

confidence: 95%

“…Let us observe that, from the scaling of C and χ, Eqs. (13,17), in the region of large time differences where the forms of Eqs. (14,18) hold, one has…”

Section: Numerical Simulationsmentioning

confidence: 99%

Role of initial state and final quench temperature on aging properties in phase-ordering kinetics

Corberi

Villavicencio-Sanchez

2016

Phys. Rev. E

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We study numerically the two-dimensional Ising model with non-conserved dynamics quenched from an initial equilibrium state at the temperature Ti ≥ Tc to a final temperature T f below the critical one. By considering processes initiating both from a disordered state at infinite temperature Ti = ∞ and from the critical configurations at Ti = Tc and spanning the range of final temperatures T f ∈ [0, Tc[ we elucidate the role played by Ti and T f on the aging properties and, in particular, on the behavior of the autocorrelation C and of the integrated response function χ. Our results show that for any choice of T f , while the autocorrelation function exponent λC takes a markedly different value for Ti = ∞ [λC (Ti = ∞) 5/4] or Ti = Tc [λC (Ti = Tc) 1/8] the response function exponents are unchanged. Supported by the outcome of the analytical solution of the solvable spherical model we interpret this fact as due to the different contributions provided to autocorrelation and response by the large-scale properties of the system. As changing T f is considered, although this is expected to play no role in the large-scale/long-time properties of the system, we show important effects on the quantitative behavior of χ. In particular, data for quenches to T f = 0 are consistent with a value of the response function exponent λχ = 1 2 λC (Ti = ∞) = 5/8 different from the one [λχ ∈ (0.5 − 0.56)] found in a wealth of previous numerical determinations in quenches to finite final temperatures. This is interpreted as due to important pre-asymptotic corrections associated to T f > 0.

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Spin Glasses

Baity‐Jesi¹

2016

Springer Theses

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How soon after a zero-temperature quench is the fate of the Ising model sealed?

Cited by 47 publications

References 25 publications

Critical percolation in the dynamics of the 2D ferromagnetic Ising model

Critical percolation in the dynamics of the 2D ferromagnetic Ising model

Role of initial state and final quench temperature on aging properties in phase-ordering kinetics

Spin Glasses

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