Domain growth in random magnets

Paul, Raja; Puri, Sanjay; Rieger, Heiko

doi:10.1209/epl/i2004-10276-4

Cited by 80 publications

(159 citation statements)

References 26 publications

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“…This has been corroborated by numerical simulations [2] as well as analytical results in exactly solvable limits [1,3]. As shown by Paul et al [4], a power law domain growth is also observed for the present disordered system, which suggests to plot, here also, C(t, t w ) as a function of t/t w : this is depicted in Fig. 3a.…”

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confidence: 87%

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Superaging in two-dimensional random ferromagnets

2007

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We study the aging properties, in particular the two-time autocorrelations, of the two-dimensional randomly diluted Ising ferromagnet below the critical temperature via Monte-Carlo simulations. We find that the autocorrelation function displays additive aging C(t, tw) = Cst(t) + Cag(t, tw), where the stationary part Cst decays algebraically. The aging part shows anomalous scaling Cag(t, tw) = C(h(t)/h(tw)), where h(u) is a non-homogeneous function excluding a t/tw scaling. PACS numbers:The phase ordering kinetics in pure systems has attracted much attention in the last years [1]. A common scenario for instance for ferromagnets after a fast quench from above to below the ordering temperature is a continuous domain growth governed by a single length scale that depends algebraically on the time t w after the quench. The existence of this length scale quite frequently determines also the scaling properties of other dynamical non-equilibrium quantities like the two-time auto-correlation function C(t, t w ), which describes the correlations between the spin configurations at the time t w after the quench and a later configuration at a time t + t w . It gives rise to what is called simple aging in the context of glassy systems [2]: C(t, t w ) depends for large times t and t w only on the scaling variable t/t w . This behavior is rather well established by analytical works in various non-random models [3], and it has been corroborated by a large amount of numerical work [2].Much less analytical results are available for disordered ferromagnets, where numerical simulations thus play an important role. A recent numerical study of the relaxational dynamics in two-dimensional random magnets [4] found evidence for a power law growth L(t) ∝ t 1/z of the aforementioned length scale L(t). The dynamical exponent z turned out to depend both on temperature T and disorder strength and to behave as z ∝ 1/T at low temperatures T . The latter is compatible with activated dynamics of pinned domain walls over logarithmic free energy barriers (rather than power law [5]). The apparent existence of a single length scale that grows algebraically was confirmed by a recent numerical work [6], where it was furthermore claimed that the response function is well described by local scale invariance [7]. In spite of this, the correlation function showed systematic deviations from a simple t/t w scaling [6] (although simple aging seems to work well in d = 3 [8]). In [6], the autocorrelation was then compared to the scaling form C(t, t w ) ∼ t −xc (t/t w ), which usually holds at a critical point with x > 0 [9]. However, a fit of this form to the numerical data obtained in [6] (and to ours as we will report below) yielded negative exponents x, which is unphysical. The aim of this paper is to suggest an alternative picture originally applied in the context of aging experiments in glasses [10] and spin glasses [11].We study the site diluted Ising model (DIM) defined on 2-dimensional square lattice with periodic boundary conditions, and described by th...

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confidence: 87%

“…A recent numerical study of the relaxational dynamics in two-dimensional random magnets [4] found evidence for a power law growth L(t) ∝ t 1/z of the aforementioned length scale L(t). The dynamical exponent z turned out to depend both on temperature T and disorder strength and to behave as z ∝ 1/T at low temperatures T .…”

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confidence: 99%

Superaging in two-dimensional random ferromagnets

2007

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“…One issue that has attracted much attention recently concerns ordering processes, relaxation phenomena, and the formation of domains in disordered systems. Examples include vortex lines in disordered type-II superconductors, [1][2][3][4][5] polymers in random media, [6][7][8][9] coarsening of disordered magnets, [10][11][12][13][14][15] and slow dynamics in spin glasses. 13,16,17 Our understanding of relaxation phenomena and aging processes in nonfrustrated systems with slow dynamics has greatly progressed during the last decade, mainly through the systematic study of critical and coarsening ferromagnets ͑see Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Monte Carlo simulations of various disordered ferromagnetic Ising models [10][11][12][13][14][15] found for the dynamical correlation length L͑t͒ a power-law increase, L͑t͒ϳt 1/z , with a nonuniversal dynamical exponent z that depends on temperature and on the nature of the disorder. This behavior can be explained by assuming that the energy barriers grow logarithmically with L. 10,11 As a consequence, it follows that the dynamical exponent z should be inversely proportional to the temperature: z ϳ 1 / T. Whereas this temperature dependence has been observed in the CardyOstlund model, 19 a careful study 14 has revealed that in the random-bond Ising model the temperature dependence of the dynamical exponent is more complicated. This fact points to the existence of conceptual problems in the approach of Paul et al 10,11 In addition, an algebraic growth law is in strong contrast to the classical theory of activated dynamics that, under the assumption of energy barriers growing as a power of L, predicts a slow logarithmic increase 20 in this length: L ϳ͑ln t͒ 1/ , with the barrier exponent Ͼ 0.…”

Section: Introductionmentioning

confidence: 99%

“…This behavior can be explained by assuming that the energy barriers grow logarithmically with L. 10,11 As a consequence, it follows that the dynamical exponent z should be inversely proportional to the temperature: z ϳ 1 / T. Whereas this temperature dependence has been observed in the CardyOstlund model, 19 a careful study 14 has revealed that in the random-bond Ising model the temperature dependence of the dynamical exponent is more complicated. This fact points to the existence of conceptual problems in the approach of Paul et al 10,11 In addition, an algebraic growth law is in strong contrast to the classical theory of activated dynamics that, under the assumption of energy barriers growing as a power of L, predicts a slow logarithmic increase 20 in this length: L ϳ͑ln t͒ 1/ , with the barrier exponent Ͼ 0. New insights into this matter have come very recently through a series of papers on the dynamics of elastic lines in a random potential.…”

Section: Introductionmentioning

confidence: 99%

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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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Local Scale-Invariance in Disordered Systems

Henkel¹,

Pleimling

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Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can describe data for either non-glassy systems quenched to below Tc or else for spin glasses at criticality. The dependence of the scaling behaviour on the distribution of the random couplings is discussed. It is shown that finite-time corrections to scaling can become quite sizable in these systems. Numerically determined ageing quantities are confronted with available experimental results.

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Domain growth in random magnets

Cited by 80 publications

References 26 publications

Superaging in two-dimensional random ferromagnets

Superaging in two-dimensional random ferromagnets

Aging in coarsening diluted ferromagnets

Local Scale-Invariance in Disordered Systems

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