Theory of dynamic critical phenomena

Hohenberg, P. C.; Halperin, Bertrand I.

doi:10.1103/revmodphys.49.435

Cited by 6,474 publications

(5,834 citation statements)

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“…We did not use the theory of finite-size scaling [22][23][24] because the calculation of critical exponents is not the purpose of the present work. However, in order to appreciate finite-size effects, we carried out simulations in the 2D case for sizes from L × L = 24 × 24 to 60 × 60 and in the case of thin films from L × L × L z = 12 × 12 × 4 to 48 × 48 × 6.…”

Section: Model and Methodsmentioning

confidence: 99%

“…They serve as testing means for new theoretical developments. Over the years, the standard MC method [21] has been improved by the finite-size scaling theory [22] and by other high-performance techniques such as histogram techniques [23,24], cluster updating algorithms [25][26][27] and Wang-Landau flat-histogram method [28]. We have now at hand these efficient techniques to deal with complex systems.…”

Section: Introductionmentioning

confidence: 99%

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Re-orientation transition in molecular thin films: Potts model with dipolar interaction

Hoang¹,

Kasperski²,

Puszkarski³

et al. 2013

J. Phys.: Condens. Matter

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We study the low-temperature behavior and the phase transition of a thin film by Monte Carlo simulation. The thin film has a simple cubic lattice structure where each site is occupied by a Potts parameter which indicates the molecular orientation of the site. We take only three molecular orientations in this paper which correspond to the 3-state Potts model. The Hamiltonian of the system includes: (i) the exchange interaction Jij between nearest-neighbor sites i and j (ii) the long-range dipolar interaction of amplitude D truncated at a cutoff distance rc (iii) a single-ion perpendicular anisotropy of amplitude A. We allow Jij = Js between surface spins, and Jij = J otherwise. We show that the ground state depends on the the ratio D/A and rc. For a single layer, for a given A, there is a critical value Dc below (above) which the ground-state (GS) configuration of molecular axes is perpendicular (parallel) to the film surface. When the temperature T is increased, a re-orientation transition occurs near Dc: the low-T in-plane ordering undergoes a transition to the perpendicular ordering at a finite T , below the transition to the paramagnetic phase. The same phenomenon is observed in the case of a film with a thickness. We show that the surface phase transition can occur below or above the bulk transition depending on the ratio Js/J. Surface and bulk order parameters as well as other physical quantities are shown and discussed.

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Section: Model and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Re-orientation transition in molecular thin films: Potts model with dipolar interaction

Hoang¹,

Kasperski²,

Puszkarski³

et al. 2013

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…By extreme type II superconductor we mean κ → ∞. In such a regime it is expected that the static critical properties at zero external field are the same as in superfluid 4 He. 1 This expectation is confirmed by experiments measuring specific heat 2 and penetration depth 3 in bulk samples of YBCO.…”

Section: Introductionmentioning

confidence: 99%

Critical dynamics, duality, and the exact dynamic exponent in extreme type-II superconductors

Nogueira

Manske

2005

Phys. Rev. B

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The critical dynamics of superconductors is studied using renormalization group and duality arguments. We show that in extreme type II superconductors the dynamic critical exponent is given exactly by z = 3/2. This result does not rely on the widely used models of critical dynamics. Instead, it is shown that z = 3/2 follows from the duality between the extreme type II superconductor and a model with a critically fluctuating gauge field. Our result is in agreement with Monte Carlo simulations and at least one experiment.

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“…As in the model H, 22,31,32) we can use Eq. (2.1) to derive where the superscript ''T'' indicates the transposition.…”

Section: Dynamicsmentioning

confidence: 99%

Drag Coefficient of a Raftlike Domain Embedded in a Fluid Membrane Being a Near-Critical Binary Mixture

Fujitani

2013

J. Phys. Soc. Jpn.

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We consider a circular liquid domain in a flat fluid membrane surrounded by three-dimensional fluids, and assume that the membrane outside the domain is a two-dimensional near-critical binary fluid mixture. The membrane viscosity outside the domain is assumed to be uniform, irrespective of the local composition, and to be the same as that of the domain. Using the Gaussian free-energy functional, we show that the drag coefficient of the domain can be decreased by the preferential attraction between the domain and a component of the mixture, unlike that of a rigid sphere in a three-dimensional near-critical binary fluid mixture studied recently.

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Theory of dynamic critical phenomena

Cited by 6,474 publications

References 257 publications

Re-orientation transition in molecular thin films: Potts model with dipolar interaction

Re-orientation transition in molecular thin films: Potts model with dipolar interaction

Critical dynamics, duality, and the exact dynamic exponent in extreme type-II superconductors

Drag Coefficient of a Raftlike Domain Embedded in a Fluid Membrane Being a Near-Critical Binary Mixture

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