Ordering dynamics in Disordered systems

Puri, Sanjay

doi:10.1080/01411590410001672611

Cited by 30 publications

(28 citation statements)

References 64 publications

(64 reference statements)

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“…This gives rise to energy barriers, which are overcome by thermally activated hopping. The barrier dependence on determines the asymptotic domain growth law [9]. Our observation that z depends linearly on f is consistent with energy barriers 040302-3 which have a logarithmic dependence on in this regime [17].…”

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confidence: 79%

“…In this context, there have been a number of studies investigating diffusion-driven coarsening in Ising systems with quenched disorder, e.g., bond, site, random-field [9][10][11][12][13][14][15][16][17][18][19][20][21]. A general observation in these studies is that trapping of domain boundaries by disorder sites [9,10] results in a slower growth of domains. It is now well established that the growth law in disordered Ising systems crosses over from a power-law behavior to a logarithmic one [20,21].…”

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confidence: 99%

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Phase separation of fluids in porous media: A molecular dynamics study

2014

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We present comprehensive molecular dynamics results for phase-separation kinetics of fluids in a porous medium. This system is modeled by a symmetric Lennard-Jones fluid mixture with a quenched random field. The presence of disorder slows down domain growth from power-law to a logarithmic form. It also modifies the correlation functions and structure factors which characterize the morphology. In particular, the structure-factor tail shows a non-Porod behavior, which is the consequence of scattering from rough interfaces.

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confidence: 79%

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confidence: 99%

Phase separation of fluids in porous media: A molecular dynamics study

2014

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“…26 These differences in the observed scaling behavior of different disordered ferromagnets remains to be explained. Finally, some coarsening ferromagnets with weak randomness 27 ͑as, for example, the random-bond or the random-field Ising models͒ have been shown to display a superuniversal behavior: scaling functions of space-and time-dependent quantities are independent of disorder and temperature provided that distances are measured in units of the dynamical correlation length L͑t͒. 28 This has been verified in various coarsening systems both for one-time 13,15,[29][30][31][32] and two-time quantities 14 but it is an open question how general this result really is.…”

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confidence: 99%

Aging in coarsening diluted ferromagnets

2010

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We comprehensively study nonequilibrium relaxation and aging processes in the two-dimensional randomsite Ising model through numerical simulations. We discuss the dynamical correlation length as well as scaling functions of various two-time quantities as a function of temperature and of the degree of dilution. For already modest values of the dynamical correlation length L deviations from a simple algebraic growth, L͑t͒ϳt 1/z , are observed. When taking this nonalgebraic growth properly into account, a simple aging behavior of the autocorrelation function is found. This is in stark contrast to earlier studies where, based on the assumption of algebraic growth, a superaging scenario was postulated for the autocorrelation function in disordered ferromagnets. We also study the scaling behavior of the space-time correlation as well as of the time integrated linear response and find again agreement with simple aging. Finally, we briefly discuss the possibility of superuniversality in the scaling properties of space-and time-dependent quantities.

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“…This protocol amounts to the instantaneous quench of the system from the initial temperature T i = ∞ to the final temperature T < T c . As it is well known, a coarsening stage is observed [5][6][7][8][9][11][12][13][14][15][16][17][18][19][20] with growing magnetic domains of size L(t, ǫ, ℓ), where ℓ is the system size and we indicate generically by ǫ the strength of the disorder. For example, denoting by L the domains size in an infinite system (L(t, ǫ) ≡ L(t, ǫ, ℓ = ∞)), in a pure (non disordered) magnet (ǫ = 0) one usually has L(t, 0) ∝ t 1/z (with z = 2 with a non-conserved order parameter).…”

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confidence: 99%

“…Since this is out of reach, we mainly focus on the limits y ≫ 1 and y ≪ 1, corresponding to the regimes w and s defined above, so that Eq. (5) simplifies to the couple of forms in (7) where the scaling functions V and ω depend on a single scaling variable. RBIM) We start this program from the RBIM.…”

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On a relation between roughening and coarsening

Corberi

Lippiello²,

Zannetti

2016

EPL

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We argue that a strict relation exists between two in principle unrelated quantities: The size of the growing domains in a coarsening system, and the kinetic roughening of an interface. This relation is confirmed by extensive simulations of the Ising model with different forms of quenched disorder, such as random bonds, random fields and stochastic dilution.PACS numbers: 05.40.-a Slow relaxation is a feature found in a variety of physical systems including randomly stirred fluids, ballistic aggregation, magnetic flux lines in superconductors [1], directed polymers and manifolds in random media [2][3][4], phase-ordering [6][7][8][9][11][12][13][14][15][16][17][18][19][20] and others. In these cases the evolution is characterized by scale-free power-law behaviors and the equilibrium state is approached on a timescale that diverges in the thermodynamic limit. In this Letter we focus on two paradigms of slow relaxation, i) the evolution a disordered ferromagnet after a temperature quench and ii) the roughening of an interface in a medium. The aim of the paper is to show a strict correspondence between i) and ii).A unified description of the two problems above can be arrived at by considering a ferromagnetic system, namely a collection of interacting Ising spins S i on the sites i of a lattice. For such a system the usual para-ferromagnetic transition occurs at some critical temperature T c . Quenched disorder, in the form of random fields or bonds, stochastic dilution or other sources of randomness, can be present provided that the low-temperature ordered phase is preserved. The two kinds of slow evolution i) and ii) mentioned above can be observed in such a model at low temperature T < T c by preparing the sample with the initial condition (at time t = 0) in the following two ways:i) The value of each spin S i = ±1 is randomly chosen and is uncorrelated from the others, corresponding to the equilibrium state of the ferromagnet at infinite temperature. This protocol amounts to the instantaneous quench of the system from the initial temperature T i = ∞ to the final temperature T < T c . As it is well known, a coarsening stage is observed [5][6][7][8][9][11][12][13][14][15][16][17][18][19][20] with growing magnetic domains of size L(t, ǫ, ℓ), where ℓ is the system size and we indicate generically by ǫ the strength of the disorder. For example, denoting by L the domains size in an infinite system (L(t, ǫ) ≡ L(t, ǫ, ℓ = ∞)), in a pure (non disordered) magnet (ǫ = 0) one usually has L(t, 0) ∝ t 1/z (with z = 2 with a non-conserved order parameter). Dynamical scaling [5] implies that L is the only dominant length at large times.ii) The system is divided into two halves, as for instance by the diagonal in a square system, and spins are set to the value S i = +1 in one half and S i = −1 in the other. Appropriate boundary conditions are provided in such a way that the spanning interface seeded by the initial condition remains at all times (e.g. if the system is divided by the diagonal anti-periodic boundary conditions are us...

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Ordering dynamics in Disordered systems

Cited by 30 publications

References 64 publications

Phase separation of fluids in porous media: A molecular dynamics study

Phase separation of fluids in porous media: A molecular dynamics study

Aging in coarsening diluted ferromagnets

On a relation between roughening and coarsening

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