Statistical mechanics of vortices from field theory (original) (raw)

Vortices in equilibrium scalar electrodynamics

1998

Scalar electrodynamics can be used to investigate the formation of cosmic strings in the early universe. We present the results of lattice Monte Carlo simulations of an effective three-dimensional U(1)+Higgs theory that describes the equilibrium properties of finite-temperature scalar electrodynamics near the transition. A gauge-invariant criterion for the existence of a vortex is used in measuring the properties of the vortex network in the equilibrium state both in the Coulomb and in the Higgs phase of the system. The naive definition of the vortex density becomes meaningless in the continuum limit and special care is needed in extracting physical quantities. Numerical evidence for a physical discontinuity in the vortex density is given.

Vortex tension as an order parameter in three-dimensional U(1) + Higgs theory

Nuclear Physics B, 1999

We use lattice Monte Carlo simulations to study non-perturbatively the tension, i.e. the free energy per unit length, of an infinitely long vortex in the three-dimensional U(1)+Higgs theory. This theory is the low-energy effective theory of hightemperature scalar electrodynamics, the standard framework for cosmic string studies. The vortex tension is measured as a function of the mass parameter at a large value of the Higgs self-coupling, where the transition between the phases is continuous. It is shown that the tension gives an order parameter that can distinguish between the two phases of the system. We argue that the vortex tension can describe the physics of long strings without lattice artifacts, unlike vortex network percolation.

Critical Dynamics of Gauge Systems: Spontaneous Vortex Formation in 2D Superconductors

Physical Review Letters, 2002

We examine the formation of vortices during the nonequilibrium relaxation of a high-temperature initial state of an Abelian-Higgs system. We equilibrate the scalar and gauge fields using gaugeinvariant Langevin equations and relax the system by instantaneously removing thermal fluctuations. For couplings near critical, κc = √ λ/e = 1, we observe the formation of large clusters of like-sign magnetic vortices. Their appearance has implications for the dynamics of the phase transition, for the distribution of topological defects and for late-time phase ordering kinetics. We offer explanations for both the observed vortex densities and vortex configurations.

Vortex description of the first-order phase transition in the two-dimensional Abelian-Higgs model

Physical Review E, 2003

We use both analytical arguments and detailed numerical evidence to show that the first-order transition in the type-I two-dimensional Abelian-Higgs model is commensurate with the statistical behavior of its vortex fluctuations, which behave as an ensemble of attractive particles. The clustering instabilities of such ensembles are shown to be connected to the process of phase nucleation. Calculations of the vortex equation of state show that the temperature for the onset of clustering is in qualitative agreement with the critical temperature. The vortex description provides a general gauge invariant mesoscopic mechanism for the first-order transition and applies for arbitrary type-I couplings.

Vortices and 2D Bosons: A Path-Integral Monte Carlo Study

Physical Review Letters, 1997

The vortex system in a high-T c superconductor has been studied numerically using the mapping to 2D bosons and the path-integral Monte Carlo method. We find a single first-order transition from an Abrikosov lattice to an entangled vortex liquid. The transition is characterized by an entropy jump ∆S ≈ 0.4 k B per vortex and layer (parameters for YBCO) and a Lindemann number c L ≈ 0.25. The increase in density at melting is given by ∆ρ = 6.0×10 −4 /λ(T) 2. The vortex liquid corresponds to a bosonic superfluid, with ρ s = ρ even in the limit λ → ∞.

Spontaneous vortex formation in the cooling dynamics of gauge systems

Vortex Densities and Correlations at Phase Transitions

Eprint Arxiv Hep Ph 9510385, 1995

We present a model for the formation of relativistic vortices (strings) at a quench, and calculate their density and correlations. The significance of these to early universe and condensed-matter physics is discussed.

Phase Structure of Electroweak Vacuum in a Strong Magnetic Field: The Lattice Results

Physical Review Letters

Using first-principle lattice simulations, we demonstrate that in the background of a strong magnetic field (around 10 20 T), the electroweak sector of the vacuum experiences two consecutive crossover transitions associated with dramatic changes in the zero-temperature dynamics of the vector W bosons and the scalar Higgs particles, respectively. Above the first crossover, we observe the appearance of large, inhomogeneous structures consistent with a classical picture of the formation of W and Z condensates pierced by vortices. The presence of the W and Z condensates supports the emergence of the exotic superconducting and superfluid properties induced by a strong magnetic field in the vacuum. We find evidence that the vortices form a disordered solid or a liquid rather than a crystal. The second transition restores the electroweak symmetry. Such conditions can be realized in the near-horizon region of the magnetized black holes.

Phase coherence and the boson analogy of vortex liquids

Physical Review B, 1998

The statistical mechanics of the flux-line lattice in extreme type-II superconductors is studied within the framework of the uniformly frustrated anisotropic three-dimensional XY -model. It is assumed that the externally applied magnetic field is low enough to invalidate the lowest Landaulevel approach to the problem. A finite-field counterpart of an Onsager vortex-loop transition in extreme type-II superconductors renders the vortex liquid phase-incoherent when the Abrikosov vortex lattice undergoes a first order melting transition. For the magnetic fields considered in this paper, corresponding to filling fractions f given by 1/f = 12, 14, 16, 20, 25, 32, 48, 64, 72, 84, 96, 112, and 128, the vortex liquid phase is not describable as a liquid of well-defined field-induced vortex lines. This is due to the proliferation of thermally induced closed vortex-loops with diameters of order the magnetic length in the problem, resulting in a "percolation transition" driven by non-field induced vortices also transverse to the direction of the applied magnetic field. This immediately triggers flux-line lattice melting and loss of phase-coherence along the direction of the magnetic field. Due to this mechanism, the field induced flux lines loose their line tension in the liquid phase, and cannot be considered to be directed or well defined. In a non-relativistic 2D boson-analogy picture, this latter feature would correspond to a vanishing mass of the bosons. Scaling functions for the specific heat are calculated in zero and finite magnetic field. From this we conclude that the critical region is of order 10% of Tc for a mass-anisotropy Mz/M = 3, and increases with increasing mass-anisotropy. The entropy jump at the melting transition is calculated in two ways as a function of magnetic field for a mass-ansitropy slightly lower than that in Y BCO, namely with and without a T -dependent prefactor in the Hamiltonian originating at the microscopic level and surfacing in coarse grained theories such as the one considered in this paper. In the first case, it is found to be ∆S = 0.1kB per pancake-vortex, roughly independent of the magnetic field for the filling fractions considered here. In the second case, we find an enhancement of ∆S by a factor which is less than 2, increasing slightly with decreasing magnetic field. This is still lower than experimental values of ∆S ≈ 0.4kB found experimentally for Y BCO using calorimetric methods. We attribute this to the slightly lower mass-anisotropy used in our simulations. 74.25.Dw, 74.25.Ha,74.60.Ec

What Becomes of Giant Vortices in the Abelian Higgs Model

Physical Review Letters

We discuss vortex solutions of the Abelian Higgs model in the limit of large winding number n. We suggest a framework where a topological quantum number n is associated with a ratio of dynamical scales and a systematic expansion in inverse powers of n is then derived in the spirit of effective field theory. The general asymptotic form of giant vortices is obtained. For critical coupling the axially symmetric vortices become integrable in the large-n limit and we present the corresponding analytic solution. The method provides simple asymptotic formulas for the vortex shape and parameters with accuracy that can be systematically improved, and can be applied to topological solitons of other models. After including the next-to-leading terms the approximation works remarkably well down to n ¼ 1.

Statistical mechanics of vortices from field theory (original) (raw)

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