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

Corberi, Federico; Villavicencio-Sanchez, Rodrigo

doi:10.1103/physreve.93.052105

Cited by 12 publications

(16 citation statements)

References 44 publications

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“…This study is also a complement to works that try to elucidate the role played by the initial conditions on the post-quench dynamics of the Ginzburg -Landau scalar field theory [55] and, more recently, the kinetic Ising model [56,57,58] as well as the influence of a non-vanishing cooling rate on the scaling properties of discrete models close to their phase transition [45]. In the latter paper the emphasis was set on the scaling properties of the order parameter and how these depend, or not, on the microscopic stochastic updates.…”

Section: Discussionmentioning

confidence: 92%

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

Ricateau¹,

Cugliandolo²,

Picco³

2018

J. Stat. Mech.

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We study, with numerical methods, the fractal properties of the domain walls found in slow quenches of the kinetic Ising model to its critical temperature. 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. arXiv:1709.05268v1 [cond-mat.stat-mech] 15 Sep 2017Since the interfaces on short length scales are not smooth anymore, their fractal dimension is given bywhere κ c = 3 is the same universal parameter as in the pre-factor in front of the logarithmic growth of the wav. Note that D c/z c ≈ 0.634 > 1 /2. The wav still has a universal behaviour, now highlighted

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Section: Discussionmentioning

confidence: 92%

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

Ricateau¹,

Cugliandolo²,

Picco³

2018

J. Stat. Mech.

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“…Beyond the case of a quench from a disordered state addressed in this paper, many other topics remains unexplored, as for instance the kinetics following a quench from a critical state [25,26], which is present in the one-dimensional model with algebraic interactions when 0 < σ ≤ 1 when T c is finite. In addition, besides the determination of the growth law L(t), several other features of the Ising model with space decaying interactions are worth of further investigations.…”

Section: A2 Fast Cop Dynamicsmentioning

confidence: 99%

One Dimensional Phase-Ordering in the Ising Model with Space Decaying Interactions

Corberi

Lippiello²,

Politi

2019

J Stat Phys

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The study of the phase ordering kinetics of the ferromagnetic one-dimensional Ising model dates back to 1963 (R.J. Glauber, J. Math. Phys. 4, 294) for non conserved order parameter (NCOP) and to 1991 (S.J. Cornell, K. Kaski and R.B. Stinchcombe, Phys. Rev. B 44, 12263) for conserved order parameter (COP). The case of long range interactions J(r) has been widely studied at equilibrium but their effect on relaxation is a much less investigated field. Here we make a detailed numerical and analytical study of both cases, NCOP and COP. Many results are valid for any positive, decreasing coupling J(r), but we focus specifically on the exponential case, J exp (r) = e −r/R with varying R > 0, and on the integrable power law case, J pow (r) = 1/r 1+σ with σ > 0. We find that the asymptotic growth law L(t) is the usual algebraic one, L(t) ∼ t 1/z , of the corresponding model with nearest neighborg interaction (z NCOP = 2 and z COP = 3) for all models except J pow for small σ: in the non conserved case when σ ≤ 1 (z NCOP = σ + 1) and in the conserved case when σ → 0 + (z COP = 4β + 3, where β = 1/T is the inverse of the absolute temperature). The models with space decaying interactions also differ markedly from the ones with nearest neighbors due to the presence of many long-lasting preasymptotic regimes, such as an exponential mean-field behavior with L(t) ∼ e t , a ballistic one with L(t) ∼ t, a slow (logarithmic) behavior L(t) ∼ ln t and one with L(t) ∼ t 1/σ+1 . All these regimes and their validity ranges have been found analytically and verified in numerical simulations. Our results show that the main effect of the conservation law is a strong slowdown of COP dynamics if interactions have an extended range. Finally, by comparing the Ising model at hand with continuum approaches based on a Ginzburg-Landau free energy, we discuss when and to which extent the latter represent a faithful description of the former.

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“…This model undergoes a second order phase transition at a critical temperature, T c , and, for J = 1, β ln (2 + √ 3) 0.66 on the honeycomb lattice. The initial condition is always taken to be a random state with no correlations, obtained by choosing s i = +1 or s i = −1 with probability 1/2 on each lattice site (long-range correlated initial conditions, as the ones of the critical Ising point fall in a different class [5,20,21,22]). Under a mapping to occupation numbers, On the left we show a 4 × 4 triangular lattice with PBC constructed from a square lattice by adding diagonal bonds.…”

Section: The Modelmentioning

confidence: 99%

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

Cited by 12 publications

References 44 publications

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

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

One Dimensional Phase-Ordering in the Ising Model with Space Decaying Interactions

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

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