Ferromagnetic ordering in the two-dimensional dipolar<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math>model

Maier, Paul; Schwabl, Franz

doi:10.1103/physrevb.70.134430

Cited by 34 publications

(60 citation statements)

References 30 publications

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“…The model described by the Ginzburg-Landau functional (1) and which we call dxy-model is instead invariant only if we rotate spin and coordinate-vectors simultaneously. With the help of this invariance we show in [1] that the dxy-model is renormalizable. The next step is to express the spins by independent coordinates of the nonlinear…”

Section: Introductionmentioning

confidence: 99%

“…Using this method one reduces the two-dimensional integrals to a single integration. For more details see [1]. Finally we derive the Callan-Symanzik equations…”

Section: Introductionmentioning

confidence: 99%

“…So we prefer to renormalize (1) in the coordinates of the nonlinear σ-model [11,13,14,16]. As the dipolar interaction violates the O(2)-symmetry the proof of renormalizability of Brézin, Zinn-Justin and Le Guillou is no longer applicable [12].…”

Section: Introductionmentioning

confidence: 99%

“…But for a more realistic model one also has to be aware of the dipolar interaction between the magnetic moments and the existence of magneto-crystalline anisotropies due to spin-orbit coupling [9,10]. Under certain conditions, when the spins prefer to order in the plane of the magnetic atoms, it is sufficient to concentrate on the isotropic exchange and the dipolar interaction and to deal with a two-component spin (for details see [1]). In this case it is possible to describe the large scale properties of the system by a continuum model…”

Section: Introductionmentioning

confidence: 99%

“…Even for the magnetic dipolar interaction, which does not favor any particular direction, magnetic fluctuations are sufficiently reduced, leading to a finite order parameter below a transition temperature. In this article we want to describe the critical properties in the ordered phase [1].…”

Section: Introductionmentioning

confidence: 99%

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Novel phase transition in two-dimensional xy-models with long-range interaction

Maier¹,

Schwabl²

2005

Condens. Matter Phys.

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The purpose of this article is to give an overview of results concerning ordering and critical properties of two-dimensional ferromagnets including the dipolar interaction. We investigate a two-dimensional xy-model extended by the dipolar interaction. Describing our system by a nonlinear σ-model and using renormalization group methods we predict a phase transition to an ordered state. This transition is due to the long-range dipolar interaction. The ferromagnetic phase is governed by a low temperature fixed-point with infinite dipolar coupling. In the critical regime we find exponential behavior for the correlation length and the order parameter in contrast to the usual power laws. The nature of the transition shows a striking similarity to the Kosterlitz-Thouless transition. We show that there is a whole class of longrange xy-models leading to such non-standard behavior. Parameterizing the divergencies in terms of the correlation length we are able to calculate the critical exponents. These exponents are correct in any loop order.

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Section: Introductionmentioning

confidence: 99%

“…Using this method one reduces the two-dimensional integrals to a single integration. For more details see [1]. Finally we derive the Callan-Symanzik equations…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Novel phase transition in two-dimensional xy-models with long-range interaction

Maier¹,

Schwabl²

2005

Condens. Matter Phys.

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Villain model with long-range couplings

Giachetti

Defenu

Ruffo

et al. 2023

J. High Energ. Phys.

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The nearest-neighbor Villain, or periodic Gaussian, model is a useful tool to understand the physics of the topological defects of the two-dimensional nearest-neighbor XY model, as the two models share the same symmetries and are in the same universality class. The long-range counterpart of the two-dimensional XY has been recently shown to exhibit a non-trivial critical behavior, with a complex phase diagram including a range of values of the power-law exponent of the couplings decay, σ, in which there are a magnetized, a disordered and a critical phase [1]. Here we address the issue of whether the critical behavior of the two-dimensional XY model with long-range couplings can be described by the Villain counterpart of the model. After introducing a suitable generalization of the Villain model with long-range couplings, we derive a set of renormalization-group equations for the vortex-vortex potential, which differs from the one of the long-range XY model, signaling that the decoupling of spin-waves and topological defects is no longer justified in this regime. The main results are that for σ < 2 the two models no longer share the same universality class. Remarkably, within a large region of its the phase diagram, the Villain model is found to behave similarly to the one-dimensional Ising model with 1/r2 interactions.

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Nature of percolation phase transition in hydration water films around immersed bodies

Men’shikov

Федичев

2009

J Struct Chem

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Ferromagnetic ordering in the two-dimensional dipolarXYmodel

Cited by 34 publications

References 30 publications

Novel phase transition in two-dimensional xy-models with long-range interaction

Novel phase transition in two-dimensional xy-models with long-range interaction

Villain model with long-range couplings

Nature of percolation phase transition in hydration water films around immersed bodies

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