Berezinskii–Kosterlitz–Thouless phase transition of 2D dilute generalized model

Sun, Yunzhou; Jiang, Liang; Xu, Si-Liu; Yi, Lin

doi:10.1016/j.physa.2009.12.023

Cited by 4 publications

(11 citation statements)

References 44 publications

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“…As the Monte Carlo simulation proceeds, physical observables of interest are computed. The critical behavior of a topological ordering transition may be determined by considering the thermodynamic response functions: heat capacity and susceptibility [12,21,26,27]. The total susceptibility of a system of N rotors is proportional to fluctuations in the order parameter: where = ån n i N i , andn i is the orientational order parameter per site i.…”

Section: D Monte Carlo Simulations 41 Methodsmentioning

confidence: 99%

“…In the vicinity of a Berezinskiĭ-Kosterlitz-Thouless transition, the susceptibility (χ) is predicted to diverge [12,21] as a function of a diverging correlation length (ζ). In the two-dimensional XY model, it follows from the relationship between χ and ζ (Kosterlitz [21] 1974), that the maximum of the susceptibility is proportional to the system size as [26,27]:…”

Section: Response Functionsmentioning

confidence: 99%

“…Using numerical Monte Carlo simulations [26,27], one can obtain the value of the critical exponent η. In particular, the peak values of χ (i.e., χ max ) scale with a power of the system size L; on a logarithmic scale [26,27], one obtains a linear fit:…”

Section: Response Functionsmentioning

confidence: 99%

“…We have performed Monte-Carlo simulations on twodimensional XY systems in order to determine the critical exponent η of the 2D BKT transition; such a study has been performed previously by a number of authors [26,27]. The peak values of the susceptibility as a function of L, for system sizes (L×L) where L=8,10,12,14,16, are plotted in figure 3 on a log-log scale.…”

Section: Response Functionsmentioning

confidence: 99%

“…It can be seen that the peak height of the specific heat does not depend on L for large enough system sizes (L=6, 7, 8), and converges to a single value. This is an indication of a topological ordering transition [27,35]. In the case of 2D BKT transitions, the fact that the specific heat is independent of the lattice size for large enough lattices [27,35] is well-known and this behavior has been used by many authors as an indication of the BKT transition character [27,35].…”

Section: Response Functionsmentioning

confidence: 99%

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SU(2) orientational ordering in restricted dimensions: evidence for a Berezinskiĭ-Kosterlitz-Thouless transition of topological point defects in four dimensions

Gorham

Laughlin

2018

J. Phys. Commun.

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We employ the theory of topological phase transitions, of the Berezinskiĭ-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial dimensions that is characterized by a quaternion n−vector (i.e., n=4) order parameter. Due to the dimensionality of the quaternion n −vector order parameter, the development of orientational order for systems that exist in four spatial dimensions must be viewed within the context of ordering in restricted dimensions. At finite temperatures, despite the development of a well-defined amplitude of the n−vector order parameter within separate regions, ordered systems that exist in restricted dimensions are prevented from developing global orientational phase-coherence as a consequence of misorientational fluctuations throughout the system. In four dimensions, this gas of misorientational fluctuations takes the form of spontaneously generated topological point defects that belong to the third homotopy group. These topological point defects must become topologically ordered in order to obtain a ground state of aligned order parameters at zero Kelvin; we argue that this topological transition belongs to the BKT universality class. We use standard 'Metropolis' Monte Carlo simulations to estimate the thermodynamic response functions, susceptibility and heat capacity, in the vicinity of the transition towards the ground state of perfectly aligned order parameters in our four-dimensional quaternion n−vector ordered model system. On lowering the temperature below a critical value, we identify a transition that results from the minimization of misorientations in the scalar phase angles throughout the system. The thermodynamic response functions obtained by Monte Carlo simulations show characteristic behavior of a topological ordering phase transition.

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Section: D Monte Carlo Simulations 41 Methodsmentioning

confidence: 99%

Section: Response Functionsmentioning

confidence: 99%

Section: Response Functionsmentioning

confidence: 99%

Section: Response Functionsmentioning

confidence: 99%

Section: Response Functionsmentioning

confidence: 99%

See 3 more Smart Citations

SU(2) orientational ordering in restricted dimensions: evidence for a Berezinskiĭ-Kosterlitz-Thouless transition of topological point defects in four dimensions

Gorham

Laughlin

2018

J. Phys. Commun.

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Monte Carlo simulations of the site-diluted three-dimensional XY model

Santos-Filho

Plascak

2011

Computer Physics Communications

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Monte Carlo simulations of theXYvectorial Blume-Emery-Griffiths model in multilayer films forHe3−He4

Santos-Filho

Plascak

2017

Phys. Rev. E

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The XY vectorial generalization of the Blume-Emery-Griffiths (XY-VBEG) model, which is suitable to be applied to the study of ^{3}He-^{4}He mixtures, is treated on thin films structure and its thermodynamical properties are analyzed as a function of the film thickness. We employ extensive and up-to-date Monte Carlo simulations consisting of hybrid algorithms combining lattice-gas moves, Metropolis, Wolff, and super-relaxation procedures to overcome the critical slowing down and correlations among different spin configurations of the system. We also make use of single histogram techniques to get the behavior of the thermodynamical quantities close to the corresponding transition temperatures. Thin films of the XY-VBEG model present a quite rich phase diagram with Berezinskii-Kosterlitz-Thouless (BKT) transitions, BKT endpoints, and isolated critical points. As one varies the impurity concentrations along the layers, and in the limit of infinite film thickness, there is a coalescence of the BKT transition endpoint and the isolated critical point into a single, unique tricritical point. In addition, when mimicking the behavior of thin films of ^{3}He-^{4}He mixtures, one obtains that the concentration of ^{3}He atoms decreases from the outer layers to the inner layers of the film, meaning that the superfluid particles tend to locate in the bulk of the system.

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Berezinskii–Kosterlitz–Thouless phase transition of 2D dilute generalized model

Cited by 4 publications

References 44 publications

SU(2) orientational ordering in restricted dimensions: evidence for a Berezinskiĭ-Kosterlitz-Thouless transition of topological point defects in four dimensions

SU(2) orientational ordering in restricted dimensions: evidence for a Berezinskiĭ-Kosterlitz-Thouless transition of topological point defects in four dimensions

Monte Carlo simulations of the site-diluted three-dimensional XY model

Monte Carlo simulations of theXYvectorial Blume-Emery-Griffiths model in multilayer films forHe3−He4

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