Kertész Line in the Three-Dimensional Compact U(1) Lattice Higgs Model

Wenzel, Sandro Christian; Bittner, Elmar; Janke, Wolfhard; Schakel, Adriaan M. J.; Schiller, A.

doi:10.1103/physrevlett.95.051601

Cited by 41 publications

(50 citation statements)

References 36 publications

(50 reference statements)

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“…[9], we argued that the phase diagram is more refined than implied by this picture. We conjectured that although analytically connected, the two ground states can be considered as two distinct phases.…”

Section: Introductionmentioning

confidence: 90%

“…We conjectured in Refs. [9,23] that along the Kertész line, percolation observables have the usual percolation exponents. In addition, we expect that the vortex network displays discontinuous behavior in the region where the phase boundary consists of a first-order transition.…”

Section: Introductionmentioning

confidence: 99%

“…[9,23] by studying the behavior of the vortex network directly. Because vortices are geometrical objects, their analysis is amenable to the methods developed in percolation theory [24].…”

Section: Introductionmentioning

confidence: 99%

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Percolation of vortices in the 3D Abelian lattice Higgs model

et al. 2008

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The compact Abelian Higgs model is simulated on a cubic lattice where it possesses vortex lines and pointlike magnetic monopoles as topological defects. The focus of this high-precision Monte Carlo study is on the vortex network, which is investigated by means of percolation observables. In the region of the phase diagram where the Higgs and confinement phases are separated by a first-order transition, it is shown that the vortices percolate right at the phase boundary, and that the first-order nature of the transition is reflected by the network. In the crossover region, where the phase boundary ceases to be first order, the vortices are shown to still percolate. In contrast to other observables, the percolation observables show finite-size scaling. The exponents characterizing the critical behavior of the vortices in this region are shown to fall in the random percolation universality class.

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Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

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Percolation of vortices in the 3D Abelian lattice Higgs model

et al. 2008

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“…An example is provided by the 3D Abelian Higgs lattice model with compact gauge field [39]. In addition to vortices, the compact model also features magnetic monopoles as topological defects.…”

Section: Discussionmentioning

confidence: 99%

“…In Ref. [39] it was argued that this phase boundary marks the location where the vortices proliferate. A well-defined and precisely located phase boundary across which geometrical objects proliferate, yet thermodynamic quantities remain nonsingular has become known as a Kertész line.…”

Section: Discussionmentioning

confidence: 99%

Two-dimensional critical Potts and its tricritical shadow

Janke

Schakel

2006

Braz. J. Phys.

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These notes give examples of how suitably defined geometrical objects encode in their fractal structure thermal critical behavior. The emphasis is on the two-dimensional Potts model for which two types of spin clusters can be defined. Whereas the Fortuin-Kasteleyn clusters describe the standard critical behavior, the geometrical clusters describe the tricritical behavior that arises when including vacant sites in the pure Potts model. Other phase transitions that allow for a geometrical description discussed in these notes include the superfluid phase transition and Bose-Einstein condensation.

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