Physics of the dynamical critical exponent in one dimension

Cordery, Robert; Sarker, Sanjoy K.; Tobochnik, Jan

doi:10.1103/physrevb.24.5402

Cited by 83 publications

(43 citation statements)

References 5 publications

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“…The physical arguments of Cordery, Sarker, and Tobochnik [11] are applicable in a straightforward manner to our generalized algorithm and yield z=2 =*ZA-(In both our algorithm and model A, the correlation time r is the time for a domain wall to move a distance equal to the correlation length £. This random walk takes a time of order £ 2 leading to z =2.…”

Section: Magnetization Systemmentioning

confidence: 94%

Critical dynamics, spinodal decomposition, and conservation laws

Annett

Banavar

1992

Phys. Rev. Lett.

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A simple acceleration algorithm for Ising systems with conserved magnetization (model B) is presented. The dynamical critical exponent and the domain growth exponent in spinodal decomposition are found to be equal to those observed for model A systems with no conservation law. Our results demonstrate that systems with global conservation laws are in the same dynamical universality class as systems with no conservation laws. PACS numbers: 64.60.Fr, 05.50.+q, 64.60.Ht, 75.40.MgThere are three principal themes in this Letter. First, a new acceleration algorithm is proposed for Ising spin systems having a conserved magnetization (model B) [1,2]. Physical arguments (for a one-dimensional system) and detailed computer simulations (in two dimensions) show that the dynamic critical exponent z (defined by the relation r-L z , where r is the correlation time and L the linear dimension of the system at criticality) for this algorithm is the same as that obtained for model A, a system with no conservation laws. Second, we have used our algorithm to study the dynamics of spinodal decomposition [3] of a 2D Ising system with conserved magnetization following the quench from a high-temperature homogeneous phase into the two-phase coexistence region. We find that in the late-time scaling regime, the exponent n characterizing the growth of the characteristic domain size R (R~~t n ) is the same as that for a model A system («•{) and different from the conventional model B result (n = j ). Third, our results are consistent with recent predictions by Bray based on renormalization-group arguments [4-6]. They thus have a bearing on the recent controversy between Bray and Tamayo and Klein [7,8] (TK). We have studied one of the two versions of the TK model and find that the TK exponent is equal to the model A result, in contradiction to their 2D computersimulation results. Our results show that global conservation laws are irrelevant in determining the dynamical universality class, as argued recently by Bray [4-6].Our algorithm for the Ising system is a generalization of Glauber dynamics for model A-it consists of single spin flips governed by the usual Metropolis [9] rules. The global conservation of magnetization at a desired value Mo (model B) is enforced by a Creutz "demon" or bag [10]. Spin flips are only allowed if the total sample magnetization after the spin flip, Af, lies in the range A/o~£< M< Mo+8. Thus our algorithm smoothly extrapolates from model A (unbounded 8) to model B (5=0). In practice, all our calculations have been carried out with A/o=0, <5 = 2. Our principal result is that the exponents z and n are independent of whether 8 = 2 or 8 is unbounded, and correspond to the model A results. Note that 5 = 2 in the thermodynamic limit is a conserved

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Section: Magnetization Systemmentioning

confidence: 94%

Critical dynamics, spinodal decomposition, and conservation laws

Annett

Banavar

1992

Phys. Rev. Lett.

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“…The probability for the latter to happen in a random-walk model is [39] p(L) = 1/L. Therefore, at constant temperature, the prefactor τ 0 of Eq.…”

Section: Case Of Uniaxial Anisotropymentioning

confidence: 99%

Thermally activated magnetization reversal in monatomic magnetic chains on surfaces studied by classical atomistic spin-dynamics simulations

Bauer

Mavropoulos

Lounis

et al. 2011

J. Phys.: Condens. Matter

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We analyze the spontaneous magnetization reversal of supported monoatomic chains of finite length due to thermal fluctuations via atomistic spin-dynamics simulations. Our approach is based on the integration of the Landau-Lifshitz equation of motion of a classical spin Hamiltonian at the presence of stochastic forces. The associated magnetization lifetime is found to obey an Arrhenius law with an activation barrier equal to the domain wall energy in the chain. For chains longer than one domain-wall width, the reversal is initiated by nucleation of a reversed magnetization domain primarily at the chain edge followed by a subsequent propagation of the domain wall to the other edge in a random-walk fashion. This results in a linear dependence of the lifetime on the chain length, if the magnetization correlation length is not exceeded. We studied chains of uniaxial and tri-axial anisotropy and found that a tri-axial anisotropy leads to a reduction of the magnetization lifetime due to a higher reversal attempt rate, even though the activation barrier is not changed.

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“…Thus, if J < J ⊥ , the two correlations lengths must cross at some temperature. The above intuitive argument (see also [10] for a similiar argument in the context of one-dimensional Ising models) does not consider the creation and annihilation of pairs of domain walls, which play an important role in the dynamics of the system. In the following, we therefore derive the exponent z from the complete dynamics of the domain walls.…”

Section: One Dimensionmentioning

confidence: 99%

Model for growth of binary alloys with fast surface equilibration

Drossel

Kardar

1997

Phys. Rev. E

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We study a simple growth model for (d + 1)-dimensional films of binary alloys in which atoms are allowed to interact and equilibrate at the surface, but are frozen in the bulk. The resulting crystal is highly anisotropic: Correlations perpendicular to the growth direction are identical to a d-dimensional two-layer system in equilibrium, while parallel correlations generally reflect the (Glauber) dynamics of such a system. For stronger in-plane interactions, the correlation volumes change from oblate to highly prolate shapes near a critical demixing or ordering transition. In d = 1, the critical exponent z relating the scaling of the two correlation lengths varies continuously with the chemical interactions.

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Physics of the dynamical critical exponent in one dimension

Cited by 83 publications

References 5 publications

Critical dynamics, spinodal decomposition, and conservation laws

Critical dynamics, spinodal decomposition, and conservation laws

Thermally activated magnetization reversal in monatomic magnetic chains on surfaces studied by classical atomistic spin-dynamics simulations

Model for growth of binary alloys with fast surface equilibration

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