Critical slowing down in the two-dimensional Ising model measured using ferromagnetic ultrathin films

Dunlavy, M. J.; Venus, D.

doi:10.1103/physrevb.71.144406

Cited by 30 publications

(30 citation statements)

References 37 publications

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“…Moreover, different update rules applied to the same model result in different values of z. The most well-known of these rules is the single-site update rule or Metropolis algorithm, which is consistent with experimental observations of the critical dynamics in an iron film [44]. The same value of z is found in the Hohenberg-Halperin model A dynamics [45] as well as in φ 4 -theory [46].…”

Section: Introductionsupporting

confidence: 76%

Classical critical dynamics in quadratically driven Kerr resonators

Verstraelen

Wouters

2020

Phys. Rev. A

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Driven-dissipative kerr lattices with two-photon driving are experimentally relevant systems known to exhibit a symmetry-breaking phase transition, which belongs to the universality class of the thermal Ising model for the parameter regime studied here. In this work, we perform finitesize scaling of this system as it is quenched to the transition and the dynamical critical exponent is found to be compatible with z ≈ 2.18 corresponding with metropolis dynamics in classical simulations. Furthermore, we show that the Liouvillian gap scales with the same exponent, similar to scaling of the Hamiltonian gap at quantum phase transitions in closed systems.

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Section: Introductionsupporting

confidence: 76%

Classical critical dynamics in quadratically driven Kerr resonators

Verstraelen

Wouters

2020

Phys. Rev. A

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“…In the wider literature, varying estimates for z, ranging between 2.0 and 2.3, have been reported [115,116]. Above value for z translates to x ≃ 0.4 and agrees surprisingly well with the O(ǫ 2 )-renormalization-group prediction of eq.…”

Section: B Critical Order-parameter Dynamicssupporting

confidence: 71%

Critical dynamics of an isothermal compressible nonideal fluid

Groß

Varnik

2012

Phys. Rev. E

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A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible non-ideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to "model A," characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed.

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“…All the measurements are qualitatively different than the susceptibility of the 2D Ising system Fe/W(110). 18,19,31,32 Even the narrower peaks in type I signals have a normalized full width at half maximum ∆T /T peak ≈ 0.050, which is more than twice the value of 0.018 observed in the second order critical transitions of Fe/W(110). This is despite the fact that the susceptibility of the latter has a substantial imaginary component.…”

Section: Experimental Methodsmentioning

confidence: 77%

“…First, it will be necessary to confirm that Imχ(T ) is not appreciable in the fitting range. Previous studies of critical transitions in 2D Ising films 18,19,33 indicate that if Imχ(T )/Reχ(T ) ≤ 0.06 in the paramagnetic region, the linear susceptibility is measured.…”

Section: Experimental Methodsmentioning

confidence: 99%

Finite-size Kosterlitz-Thouless transition in 2DXY Fe/W(001) ultrathin films

et al. 2019

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Magnetic susceptibility measurements of 3-4 ML Fe/W(001) ferromagnetic films demonstrate that this is a 2DXY system in which a finite-size Kosterlitz-Thouless (KT) transition occurs. The films are grown in ultrahigh vacuum and their magnetic response is measured using the magneto-optic Kerr effect (MOKE). The analysis of many independently grown films shows that the paramagnetic tail of the susceptibility is described by χ(T ) = χ0 exp B/(T /TKT − 1) a , where a = 0.50 ± 0.03 and B = 3.48 ± 0.16, in quantitative agreement with KT theory. Below the finite-size transition temperature TC (L), the behaviour is complicated by dissipation (likely related to the re-emergence of four-fold anisotropy and magnetic domains). A subset of measurements with very small dissipation most closely represents the idealized system treated by theory. For these measurements, there is a temperature interval of order tens of K between the fitted Kosterlitz-Thouless transition temperature and the finite-size transition temperature, in agreement with theory. The normalized interval TC (L)/TKT − 1 = 0.065 ± 0.016 yields an estimate of the finite size L affecting the film of order micrometers. This gives experimental support to the idea that even a mesoscopic limitation of the vortex-antivortex gas results in a substantial finite-size effect at the KT transition. In contrast, fitting the paramagnetic tail to a power law, appropriate to a second order critical transition, gives unphysical parameters. The effective critical exponent γ ef f ≈ 3.7 ± 0.7 does not correspond to a known universality class, and the fitted transition temperature, Tγ, is much further below the peak in the susceptibility than is physically reasonable. * [corresponding author] venus@physics.mcmaster.ca 1 V. L. Berezinskii, Sov. Phys. -JEPT 32, 493 (1971).

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Critical slowing down in the two-dimensional Ising model measured using ferromagnetic ultrathin films

Cited by 30 publications

References 37 publications

Classical critical dynamics in quadratically driven Kerr resonators

Classical critical dynamics in quadratically driven Kerr resonators

Critical dynamics of an isothermal compressible nonideal fluid

Finite-size Kosterlitz-Thouless transition in 2DXY Fe/W(001) ultrathin films

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