Vortices in the 2d classical XY-model: a microcanonical Monte Carlo simulation study

Ota, Smita

doi:10.1016/0375-9601(95)00588-t

Cited by 5 publications

(10 citation statements)

References 24 publications

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“…We have estimated the vortex-antivortex pair creation energy for the 2D XY model as E 2DXY pair (a) ≃ 6.6J (in contrast to π 2 J ≃ 9.9J of the Villain model), which is in reasonable agreement with the results of the recent Monte Carlo simulations [8], [7] (7.55J and 7.3J, respectively). sin k x X cos k y Y , (A1)…”

Section: Discussionsupporting

confidence: 87%

“…On the contrary, the corresponding energy which we estimate for the 2D XY model turns out to deviate from the logarithmic law at small separations. In particular, our result for the energy needed to create a vortexantivortex pair is approximately 6.6J (J is the coupling constant), in contrast to 9.9J of the Villain model [6], and in reasonable agreement with the recent results of Monte Carlo simulations [7,8].…”

Section: A Spin Vorticessupporting

confidence: 91%

“…2): E 2DXY pair (a). The microcanonical Monte Carlo simulations showed that E 2DXY pair (a) ≃ 7.3J [7], while the canonical MC simulations gave 7.55J [8]. Our estimation which follows from ( 18) is E 2DXY pair (a) ≃ 6.6J, in reasonable agreement with the mentioned computer experiments (the exact result for the Villain model is π 2 J ≃ 9.9J, see (15)).…”

Section: Vortices In the Villain And 2d Xy Models A Topological Charg...supporting

confidence: 87%

“…An analogue of the condition (7) for the field ψ r , which would assure that H ϕ,ψ = 0 in the diluted Villain model (20), reads as c r u (ψ r − ψ r+u − 2πm r,r+u ) c r+u = 0 for all r .…”

Section: A Vortex Pinned By the Vacancymentioning

confidence: 99%

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Spin vortices and vacancies: Interactions and pinning on a square lattice

Kapikranian

Holovatch

2010

Phys. Rev. B

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The study gives a decisive answer to the recently risen question about the type and origin of interaction between spin vortices and spin vacancies in 2D spin models. The approach is based on the low-temperature approximation of the 2D XY model known as the Villain model and does not involve any additional approximations, thus preserving the lattice structure. The exact form of the Hamiltonian describing a system of topological charges and a vacant site supports the attractive type of interaction between the vacancy and the charges.The quantitative difference between the characteristics of the vortex behavior in the 2D XY and Villain models due to the different energy of the vortex "cores" in the two models is pointed out. This leads to a conclusion that the interaction between a vortex and a spin vacancy and between a vortex and the antivortex differs quantitatively for small separations in the two mentioned models.

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Section: Discussionsupporting

confidence: 87%

Section: A Spin Vorticessupporting

confidence: 91%

Section: Vortices In the Villain And 2d Xy Models A Topological Charg...supporting

confidence: 87%

Section: A Vortex Pinned By the Vacancymentioning

confidence: 99%

See 2 more Smart Citations

Spin vortices and vacancies: Interactions and pinning on a square lattice

Kapikranian

Holovatch

2010

Phys. Rev. B

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“…The energy needed to create a vortex-anti-vortex pair (2μ) can be estimated from the expected exponential temperature dependence of vortex density: V~e -2μ/T [18]. We obtain a value of 2μ = 7.3 [57]. The low temperature value of 2μ corresponds to the energy associated with the closest bound vortex-anti-vortex pair.…”

Section: Introductionmentioning

confidence: 94%

Nature of First-Order Transition in Planar Rotator Model with Modified Potential

Ota¹

2013

JMP

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We have carried out micro-canonical Monte Carlosimulations of a planar rotator model in 30 × 30 lattice using periodic boundary conditions. The energy distribution of the rotator in the lattice shows features that can be associated with spin wave and vortex excitations. The results supplement the first-order transition observed in canonicalMonte Carlosimulation, due to vortex nucleation. We also see features that can be associated with the in-homogeneity of vortex charge in the critical region.

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Microcanonical Monte Carlo simulations of the first-order transition in the two-dimensional Potts model

Ota

2000

J. Phys.: Condens. Matter

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Microcanonical Monte Carlo simulations have been implemented in the two-dimensional (2D) q -state Potts model. The ergodicity of this simulation technique for the Potts model is studied. It does not seem to depend on the value of q . A lack of ergodicity for small values of the system energy is reported and discussed. It has been found that the temperature dependences of physical quantities exhibit an `S'-shaped nature at the first-order transition. The degree of `S'-shaped nature was enhanced by increasing q and reducing the system size. We believe on the basis of our computer simulations that the `S' shape represents the equilibrium behaviour of a finite isolated system.

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Vortices in the 2d classical XY-model: a microcanonical Monte Carlo simulation study

Cited by 5 publications

References 24 publications

Spin vortices and vacancies: Interactions and pinning on a square lattice

Spin vortices and vacancies: Interactions and pinning on a square lattice

Nature of First-Order Transition in Planar Rotator Model with Modified Potential

Microcanonical Monte Carlo simulations of the first-order transition in the two-dimensional Potts model

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