Percolation of Vortices in the 3D Abelian Lattice Higgs Model

Abstract

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.

arXiv comment24 pages, 12 figures

References in corpus (20)

• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• The Electroweak Phase Transition: A Non-Perturbative Analysis
• Scaling corrections: site-percolation and Ising model in three dimensions
• High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers
• A Measure of data-collapse for scaling
• Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation transition
• Center vortices of Yang-Mills theory at finite temperatures
• Kertesz Line in the Three-Dimensional Compact U(1) Lattice Higgs Model
• Embedded Topological Defects in Hot Electroweak Theory: a Lattice Study
• Z-Vortex Percolation in the Electroweak Crossover Region
• String Breaking and Monopoles: a Case Study in the 3D Abelian Higgs Model
• Phase Transitions in QCD
• O(2) symmetry breaking vs. vortex loop percolation
• Center Dominance in SU(2) Gauge-Higgs Theory
• Monopole Chains in the Compact Abelian Higgs Model with doubly-charged Matter Field
• Vortex critical behavior at the de-confinement phase transition
• Vortex-line percolation in the three-dimensional complex |psi|^4 model
• High-temperature series expansions for the $q$-state Potts model on a hypercubic lattice and critical properties of percolation
• Phase Structure and Gauge Boson Propagator in the radially active 3D compact Abelian Higgs Model
• Three Phases in the 3D Abelian Higgs Model with Nonlocal Gauge Interactions

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