Finite-Size Scaling in Thin Fe/Ir(100) Layers

Henkel, Malte; Andrieu, S.; Bauer, Philippe; Piécuch, M.

doi:10.1103/physrevlett.80.4783

Cited by 49 publications

(51 citation statements)

References 20 publications

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“…The Heuer's estimate was z = 2.4(1) and the difference with our estimate z = 2.62(7) is z off−eq − z eq = 0.22 (12), i.e. 1.8 standard deviations.…”

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confidence: 77%

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Universality in the off-equilibrium critical dynamics of the three-dimensional diluted Ising model

1999

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We study the off-equilibrium critical dynamics of the three dimensional diluted Ising model. We compute the dynamical critical exponent z and we show that it is independent of the dilution only when we take into account the scaling-corrections to the dynamics. Finally we will compare our results with the experimental data.PACS numbers: 05.50.+q, 75.10.Nr, 75.40.Mg The issue of Universality in disordered systems is a controversial and interesting subject.Very often in the past it has been argued that critical exponents change with the strength of the disorder [1]. While, on a deeper analysis, it has turned out that those exponents were "effective" ones, i.e. they are affected by strong scaling corrections. So, when one studies the critical behavior of a disordered system it is mandatory to control the leading correction-to-scaling in order to avoid these effects that could modify the dilution-independent values of the critical exponents. For instance, in Ref.[2] the equilibrium critical behavior of the three dimensional diluted Ising model was studied. The authors showed that taking into account the corrections-to-scaling it was possible to show that the static critical exponents (e.g. ν and η) and cumulants were dilution-independent. These numerical facts supports the (static) perturbative renormalization group picture: all the points of the critical line (with p < 1) belong to the same Universality class (with critical exponents given by the random fixed point) [3]. Their final values of the exponents [2] were in very good agreement with the experimental figures (see below).We will show that an analogous effect also happens in the off-equilibrium dynamics of the diluted ferromagnetic model and we will take it into account in our data analysis, in order to get the best estimate of the critical dynamical exponent.The critical dynamics of the diluted Ising model has been studied experimentally in Ref.[4] using neutron spin-echo inelastic scattering on samples of Fe 0.46 Zn 0.54 F 2 (antiferromagnetic diluted model) and has been compared with the results obtained in pure samples (FeF 2 ) [4]. For the pure model a dynamical critical exponent z = 2.1(1) was found (in good agreement with the theoretical predictions based on one-loop perturbative renormalization group (PRG) [5]) whereas in the diluted case the exponent z = 1.7(2) was computed (three standard deviations away of the analytical prediction based on (one-loop) PRG that provides z ≃ 2.34 [6]). Furthermore, the dynamical exponent was computed in the framework of the PRG up to two loops and it was obtained z = 2.237 [7] and z = 2.180 [8] (the experimental value is at 2.5 standard deviation of the two loops analytical result).In the experiment [4] were measured critical amplitudes 100 times smaller than those computed in the pure case. It is clear that a more precise experiment on this issue will be welcome. We should point out that the critical dynamics of a diluted antiferromagnet is the same as of a diluted ferromagnet.A numerical study of the on-equilibr...

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“…The Heuer's estimate was z = 2.4(1) and the difference with our estimate z = 2.62(7) is z off−eq − z eq = 0.22 (12), i.e. 1.8 standard deviations.…”

contrasting

confidence: 77%

“…[11]). The second one is that the correction-to-scaling exponent can be (and it has been) computed in a real experiment [12].…”

mentioning

confidence: 99%

Universality in the off-equilibrium critical dynamics of the three-dimensional diluted Ising model

1999

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“…26,27 , while an experimental measure reported in Ref. 28 yields θ = 0.57 (9). In the case of the bcc lattice, as an example of our extrapolation procedure, we have reported in Table 1 the last eight terms of the sequence (β c ) n and the results of the initial extrapolation of the last six successive alternate pairs of terms.…”

Section: A Estimates Of the Critical Pointsmentioning

confidence: 89%

Extension to orderβ23of the high-temperature expansions for the spin-12Ising model on simple cubic and body-center

Butera

Comi

2000

Phys. Rev. B

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Using a renormalized linked-cluster-expansion method, we have extended to order β 23 the high-temperature series for the susceptibility χ and the second-moment correlation length ξ of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of χ and ξ. Our best estimates for the inverse critical temperatures are β sc c = 0.221654(1) and β bcc c = 0.1573725(6). For the susceptibility exponent we get γ = 1.2375(6) and for the correlation length exponent ν = 0.6302(4). The ratio of the critical amplitudes of χ above and below the critical temperature is estimated to be C+/C− = 4.762(8). The analogous ratio for ξ is estimated to be f+/f− = 1.963(8). For the correction-to-scaling amplitude ratio we obtain a + ξ /a + χ = 0.87(6).

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“…The temperature shift has been observed in numerous experimental studies and it has also been investigated extensively in theory [78,79,80,81,82]. For thick films with L layers, the deviation from the bulk critical temperature T c (∞) is described by the well-known finite-size scaling relation [83] …”

Section: Thin Filmsmentioning

confidence: 99%

Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

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Abstract. In the past perfect surfaces have been shown to yield a local critical behaviour that differs from the bulk critical behaviour. On the other hand surface defects, whether they are of natural origin or created artificially, are known to modify local quantities. It is therefore important to clarify whether these defects are relevant or irrelevant for the surface critical behaviour.The purpose of this review is two-fold. In the first part we summarise some of the important results on surface criticality at perfect surfaces. Special attention is thereby paid to new developments as for example the study of surface critical behaviour in systems with competing interactions or of surface critical dynamics. In the second part the effect of surface defects (presence of edges, steps, quenched randomness, lines of adatoms, regular geometric patterns) on local critical behaviour in semi-infinite systems and in thin films is discussed in detail. Whereas most of the defects commonly encountered are shown to be irrelevant, some notable exceptions are highlighted. It is shown furthermore that under certain circumstances non-universal local critical behaviour may be observed at surfaces.

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Finite-Size Scaling in Thin Fe/Ir(100) Layers

Cited by 49 publications

References 20 publications

Universality in the off-equilibrium critical dynamics of the three-dimensional diluted Ising model

Universality in the off-equilibrium critical dynamics of the three-dimensional diluted Ising model

Extension to orderβ23of the high-temperature expansions for the spin-12Ising model on simple cubic and body-center

Critical phenomena at perfect and non-perfect surfaces

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