Extinction of the Berezinskii-Kosterlitz-Thouless phase transition by nonmagnetic disorder in planar symmetry spin models

Wysin, G. M.; Pereira, A. R.; Marques, Ivo de Almeida; Leonel, S. A.; Coura, P. Z.

doi:10.1103/physrevb.72.094418

Cited by 50 publications

(88 citation statements)

References 46 publications

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“…They found that the apparent ill behavior obtained by Leonel et al [21] was a fake, probably due to a poor statistics. This was confirmed by other result [23]. We did a much more careful numerical study [25] using lattice sizes L × L, from L = 16 up to L = 1280, which is a much larger range than those used so far.…”

Section: Introductionsupporting

confidence: 84%

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Kosterlitz-Thouless Transition: The Diluted XY model

Costa¹,

Lima²,

Coura³

et al. 2014

J. Phys.: Conf. Ser.

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Abstract. The effect of nonmagnetic disorder on Berezinskii-Kosterlitz-Thouless (BKT) transition in the two-dimensional ferromagnetic XY model on a square lattice, diluted by randomly placed vacancies can be an important source of information on the role played by vortexes in this transition. The transition temperature TBKT is determined as a function of vacancy density ρv by stiffness ρ and for different size of the lattice. The anomalous behavior for TBKT when ρv is close to the square lattice percolation limit is a consequence of the effect of finite size of lattice and not due the quantum fluctuations as concluded in literature. We obtain that TBKT falls to zero at ρv ≈ 0.40 close to the value 0.41 obtained for the classic model.

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Section: Introductionsupporting

confidence: 84%

“…This result is in flagrant disagreement with Refs. [22,23] and the Harris argument [18]. The work done by Young-Je et al [24] measuring the current-voltage in a site diluted Josephson junction arrays takes into account the quantum behavior of the system.…”

Section: Introductionmentioning

confidence: 99%

Kosterlitz-Thouless Transition: The Diluted XY model

Costa¹,

Lima²,

Coura³

et al. 2014

J. Phys.: Conf. Ser.

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“…This issue is addressed in [35][36][37][38]. According to the Harris criterion, disorder does not change the leading scaling behaviour of a model if the critical exponent α associated with the specific heat of the pure model is negative [39].…”

Section: The Diluted Xy Modelmentioning

confidence: 99%

Homotopy in statistical physics

Kenna¹

2006

Condens. Matter Phys.

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In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction to the mathematical methods involved in topology and homotopy theory, the role of the latter in a number of mainly low-dimensional statistical-mechanical systems is outlined. Some recent activities in this area are reviewed and some possible future directions are discussed.

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“…[14] To proceed, we attempt to locate the BKT transition temperature T c . Usually, T c can be determined by the finite-size magnetization and the helicity modulus in Fig.1, while in Fig.2 the peak of susceptibility is not used to locate T c for lack of accuracy, [14,18] and the peak of specific heat occurs a certain percent above T c . [19] The universal critical behavior of finite size induced magnetization, [4] …”

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confidence: 99%

Berezinskii—Kosterlitz—Thouless Transition in a Two-Dimensional Random-Bond XY Model on a Square Lattice

Deng¹,

Gu²

2014

Chinese Phys. Lett.

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We perform Monte Carlo simulations to study the two dimensional random-bond XY model on a square lattice. Two kinds of bond randomness with the coupling coefficient obeying the Gaussian or uniform distribution are discussed. It is shown that the two kinds of disorder lead to similar thermodynamic behaviors if their variances take the same value. This result implies that the variance can be chosen as a characteristic parameter to evaluate the strength of the randomness. In addition, the Berezinskii-Kosterlitz-Thouless transition temperature decreases as the variance increases and the transition can even be destroyed as long as the disorder is strong enough.PACS numbers: 75.50. Lk, 75.40.Mg, 05.70.Fh, 05.70.Jk The Berezinskii-Kosterlitz-Thouless (BKT) transition in two dimensional system has been extensively studied for decades since the discovery of the exotic quasi-longrange order formed by the binding of vortex-antivortex pairs. [1,2] The simplest model to demonstrate the BKT transition is the so-called 2-Dimensional (2D) XY model and the Hamiltonian takes the formwheredonates spin at site i. J ij is the coupling coefficient of the two nearestneighboring sites, i and j, and θ ij = θ i − θ j is the phase difference between the two sites. Typically, the transition in the 2D XY model is characterized by low temperature power-law decay of a two-point correlation function which gives rise to divergent susceptibility, [3] measurable finite-size-induced magnetization with universal magnetic exponent[4] and a discontinuous jump to zero of the helicity modulus. [5] In experiments, the BKT transition has been confirmed in various real systems such as 4 He films,[6] Josephson-junction arrays [6] and planar lattice of Bose-Einstein condensates. [8] Due to the presence of defects and distortions, real systems are always imperfect and usually subject to certain disorder effects. Therefore it is of interest to study how the imperfection affects on the BKT transition. For the 2D XY model, the imperfection can be demonstrated by two parameters, J ij and θ ij . J ij (or θ ij ) may be governed by a random distribution P (J ij ) (or P (θ ij )). It means that J ij (or θ ij ) takes the values subject to a probability distribution, which is called the bond randomness (or phase randomness).Rubinstein, Shraiman, and Nelson studied 2D XY ferromagnets with random Dzyaloshinskii-Moriya interactions and derived a model with both J ij and θ ij randomness.[9] They showed that the spatial variation in † Corresponding author: qgu@ustb.edu.cn J ij might be irrelevant at long wavelengths. For this reason, less attention was paid on this type of disorder. However, the case that J ij obeys a discrete probability distribution has still been intensively studied. A simple choice of [10][11][12] which means each bond might be vacant with probability 1 − p. This model is often referred to as the bond diluted model.In fact, the continuous bond randomness case that J ij obeys a continuous probability distribution should not be neglected. Korshunov arg...

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Extinction of the Berezinskii-Kosterlitz-Thouless phase transition by nonmagnetic disorder in planar symmetry spin models

Cited by 50 publications

References 46 publications

Kosterlitz-Thouless Transition: The Diluted XY model

Kosterlitz-Thouless Transition: The Diluted XY model

Homotopy in statistical physics

Berezinskii—Kosterlitz—Thouless Transition in a Two-Dimensional Random-Bond XY Model on a Square Lattice

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