arXiv subjects

M. Karjalainen

Publications and source records attributed to M. Karjalainen.

23 records · Page 2Linked to original sources

arXiv1998

Vortices in equilibrium scalar electrodynamics

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.

hep-lat↗

arXiv1998

Thermodynamics of Gauge-Invariant U(1) Vortices from Lattice Monte Carlo Simulations

We study non-perturbatively and from first principles the thermodynamics of vortices in 3d U(1) gauge+Higgs theory, or the Ginzburg-Landau model, which has frequently been used as a model for cosmological topological defect formation. We discretize the system and introduce a gauge-invariant definition of a vortex passing through a loop on the lattice. We then study with Monte Carlo simulations the total vortex density, extract the physically meaningful part thereof, and demonstrate that it has a well-defined continuum limit. The total vortex density behaves as a pseudo order parameter, having a discontinuity in the regime of first order transitions and behaving continuously in the regime of second order transitions. Finally, we discuss further gauge-invariant observables to be measured.

hep-ph↗

arXiv1997

Three-dimensional U(1) gauge+Higgs theory as an effective theory for finite temperature phase transitions

We study the three-dimensional U(1)+Higgs theory (Ginzburg-Landau model) as an effective theory for finite temperature phase transitions from the 1 K scale of superconductivity to the relativistic scales of scalar electrodynamics. The relations between the parameters of the physical theory and the parameters of the 3d effective theory are given. The 3d theory as such is studied with lattice Monte Carlo techniques. The phase diagram, the characteristics of the transition in the first order regime, and scalar and vector correlation lengths are determined. We find that even rather deep in the first order regime, the transition is weaker than indicated by 2-loop perturbation theory. Topological effects caused by the compact formulation are studied, and it is demonstrated that they vanish in the continuum limit. In particular, the photon mass (inverse correlation length) is observed to be zero within statistical errors in the symmetric phase, thus constituting an effective order parameter.

hep-lat↗

arXiv1997

Masses and Phase Structure in the Ginzburg-Landau Model

We study numerically the phase structure of the Ginzburg-Landau model, with particular emphasis on mass measurements. There is no local gauge invariant order parameter, but we find that there is a phase transition characterized by a vanishing photon mass. For type I superconductors the transition is of 1st order. For type II 1st order is excluded by susceptibility analysis, but the photon correlation length suggests 2nd order critical behaviour with ν~ 1/2. The scalar mass, in contrast, does not show clear critical behaviour in the type II regime for V \to \infty, contrary to the conventional picture.

cond-mat.supr-con↗

arXiv1996

The order of the phase transition in 3d U(1)+Higgs theory

We study the order of the phase transition in the 3d U(1)+Higgs theory, which is the Ginzburg-Landau theory of superconductivity. We confirm that for small scalar self-coupling the transition is of first order. For large scalar self-coupling the transition ceases to be of first order, and a non-vanishing scalar mass suggests that the transition may even be of higher than second order.

hep-lat↗