Monte Carlo study of the critical temperature for the planar rotator model with nonmagnetic impurities

Leonel, S. A.; Coura, P. Z.; Pereira, A. R.; Mól, L. A. S.; Costa, B. V.

doi:10.1103/physrevb.67.104426

Cited by 38 publications

(51 citation statements)

References 15 publications

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“…However, for d = 2 regular lattices, the percolation threshold (the density of vacancies required to disconnect the lattice) is ρ ≈ 0.41. Thus the work of [36] suggests that, indeed, the critical temperature vanishes before the percolation threshold is reached. In a later study, however, Berche et al suggested that the critical site-density is closer to the percolation threshold [37].…”

Section: The Diluted Xy Modelmentioning

confidence: 99%

“…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%

“…The vanishing of the critical temperature then gives the critical vacancy density in that model. In [36] the critical temperature was reported to vanish at site-vacancy density ρ ≈ 0.3. However, for d = 2 regular lattices, the percolation threshold (the density of vacancies required to disconnect the lattice) is ρ ≈ 0.41.…”

Section: The Diluted Xy Modelmentioning

confidence: 99%

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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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Section: The Diluted Xy Modelmentioning

confidence: 99%

Section: The Diluted Xy Modelmentioning

confidence: 99%

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Homotopy in statistical physics

Kenna¹

2006

Condens. Matter Phys.

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“…They found (ρ − ρ percolation ) ν , with ν = 1.56024. More recently Leonel et al [21] obtained the phase diagram T BKT × p for the site diluted model. Here, p is the density of magnetic sites.…”

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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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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“…[21][22][23] had studied the effects of nonmagnetic impurities on the KT transition. Since nonmagnetic impurities can be viewed as lattice vacancies, the results found that the KT transition disappears as the vacancy density reaches the lattice percolation limit.…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of two-dimensional spin systems under the random-bond six-state clock model

Huang

2012

Journal of Applied Physics

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The critical behavior of the clock model in two-dimensional square lattice is studied numerically using Monte Carlo method with Wolff algorithm. The Kosterlitz-Thouless (KT) transition is observed in the six-state clock model, where an intermediate phase exists between the low-temperature ordered phase and the high-temperature disordered phase. The bond randomness is introduced to the system by assuming a Gaussian distribution for the coupling coefficients with the mean μ=1 and different values of variance, from σ2=0.1 to σ2=3.0. An abrupt jump in the helicity modulus at the transition, which is the key characteristic of the KT transition, is verified with a stability argument. The critical temperature Tc for both pure and disordered systems is determined from the critical exponent η(Tc)=1/4. The results showed that a small amount of disorder (small σ) reduces the critical temperature of the system, without altering the nature of transition. However, a larger amount of disorder changes the transition from the KT-type into that of non-KT-type.

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Monte Carlo study of the critical temperature for the planar rotator model with nonmagnetic impurities

Cited by 38 publications

References 15 publications

Homotopy in statistical physics

Homotopy in statistical physics

Kosterlitz-Thouless Transition: The Diluted XY model

Critical behavior of two-dimensional spin systems under the random-bond six-state clock model

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