Role of Vortex Strings in the Three-Dimensional O(2) Model

Kohring, G.A.; Shrock, Robert; Wills, Peter

doi:10.1103/physrevlett.57.1358

Cited by 135 publications

(70 citation statements)

References 25 publications

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“…Our results fully support the theory of defect formation resulting from the critical dynamics of second order transitions [5] and all known thermodynamic results for vortex strings in O(N ) theories [13][14][15]12]. In face of this evidence we are lead to conclude that arguments singling out a special energy scale T G = T c , which would play an important role in defect formation rely on assumptions that are not realized in the true (thermo)dynamics of our model and are thus invalid.…”

Section: Discussionsupporting

confidence: 75%

“…in contact with a heat bath at a given temperature T . This model has the advantage of having been extensively studied in thermal equilibrium [13,14,12,15] and moreover of describing the thermodynamics of 4 He at criticality [16] by permitting the computation of relevant critical exponents with extreme accuracy.…”

Section: Langevin and Fokker-planck Field Dynamicsmentioning

confidence: 99%

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Ginzburg regime and its effects on topological defect formation

2000

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The Ginzburg temperature has historically been proposed as the energy scale of formation of topological defects at a second order symmetry breaking phase transition. More recently alternative proposals which compute the time of formation of defects from the critical dynamics of the system [5], have been gaining both theoretical and experimental support. We investigate, using a canonical model for string formation, how these two pictures compare. In particular we show that prolonged exposure of a critical field configuration to the Ginzburg regime results in no substantial suppression of the final density of defects formed. These results dismiss the recently proposed role of the Ginzburg regime in explaining the absence of topological defects in 4 He pressure quench experiments.

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Section: Discussionsupporting

confidence: 75%

Section: Langevin and Fokker-planck Field Dynamicsmentioning

confidence: 99%

Ginzburg regime and its effects on topological defect formation

2000

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“…Hence, the noncollinear XY magnets in d = 3 dimensions possess Z-vortex lines in addition to the Z 2 chiral domain walls, while the noncollinear Heisenberg magnets possess Z 2 -vortex lines. Although it is possible and enlightening to understand the nature of the three-dimensional transitions also as defected-mediated [60], we follow more standard theoretical approaches in this article in which these topological defects do not show up in an explicit way. §4.…”

Section: (B) Helimagnetsmentioning

confidence: 99%

Untitled

Kawamura¹

1998

J. Phys.: Condens. Matter

341

470

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Recent theoretical and experimental studies on the critical properties of frustrated antiferromagnets with the noncollinear spin order, including stacked-triangular antiferromagnets and helimagnets, are reviewed. Particular emphasis is put on the novel critical and multicritical behaviors exhibited by these magnets, together with an important role played by the 'chirality'. §1. Introduction Phase transitions and critical phenomena have been a central issue of statistical physics for many years. In particular, phase transitions of magnets or of 'spin systems' have attracted special interest. Thanks to extensive theoretical and experimental studies, we now have rather good understanding of the nature of phase transitions of standard ferromagnets and antiferromagnets. By the term 'standard', I mean here regular and unfrustrated magnets without quenched disorder and frustration. They include ferromagnets and unfrustrated antiferromagnets with the collinear spin order.One key notion which emerged through these studies is the notion of universality. According to the universality hypothesis, a variety of continuous (or secondorder) phase transitions can be classified into a small number of universality classes determined by a few basic properties characterizing the system under study, such as the space dimensionality d, the symmetry of the order parameter and the range of interaction. If one is interested only in the so-called universal quantities, such as critical exponents, amplitude ratios and scaled equation of state, various phase transitions should exhibit exactly the same behavior. In the case of standard bulk magnets in three spatial dimensions (d = 3), universality class is basically determined by the number of the spin components, n. Physically, the index n is related to the type of magnetic anisotropy: Namely, n = 1 (Ising), n = 2 (XY ) and n = 3 (Heisenberg) correspond to magnets with easy-axis-type anisotropy, easy-plane-type anisotropy and no anisotropy (isotropic magnets), respectively. The critical properties associated with these n-component O(n) universality classes have been extensively studied and are now rather well understood. From the renormalization-group (RG) viewpoint, these critical properties are governed by the so-called Wilson-Fisher O(n) fixed point.

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“…The simplest vortex-related quantity is now [22] O tot = |n ij,x | . It has the interpretation of the total vortex density, independent of their length.…”

Section: Observablesmentioning

confidence: 99%

O(2) symmetry breaking versus vortex loop percolation

Kajantie¹,

Laine²,

Neuhaus³

et al. 2000

Physics Letters B

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We study with lattice Monte Carlo simulations the relation of global O(2) symmetry breaking in three dimensions to the properties of a geometrically defined vortex loop network. We find that different definitions of constructing a network lead to different results even in the thermodynamic limit, and that with typical definitions the percolation transition does not coincide with the thermodynamic phase transition. These results show that geometrically defined percolation observables need not display universal properties related to the critical behaviour of the system, and do not in general survive in the field theory limit.

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Role of Vortex Strings in the Three-Dimensional O(2) Model

Cited by 135 publications

References 25 publications

Ginzburg regime and its effects on topological defect formation

Ginzburg regime and its effects on topological defect formation

Untitled

O(2) symmetry breaking versus vortex loop percolation

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