arXiv subjects

A. Rajantie

Publications and source records attributed to A. Rajantie.

48 records · Page 3Linked to original sources

arXiv1999

Statistical mechanics of vortices from field theory

We study with lattice Monte Carlo simulations the interactions and macroscopic behaviour of a large number of vortices in the 3-dimensional U(1) gauge+Higgs field theory, in an external magnetic field. We determine non-perturbatively the (attractive or repelling) interaction energy between two or more vortices, as well as the critical field strength H_c, the thermodynamical discontinuities, and the surface tension related to the boundary between the Meissner phase and the Coulomb phase in the type I region. We also investigate the emergence of vortex lattice and vortex liquid phases in the type II region. For the type I region the results obtained are in qualitative agreement with mean field theory, except for small values of H_c, while in the type II region there are significant discrepancies. These findings are relevant for superconductors and some models of cosmic strings, as well as for the electroweak phase transition in a magnetic field.

hep-lat↗

arXiv1999

Abelian hard thermal loops on a lattice

In Abelian theories, one can write for the hard thermal loop equations of motions a local formulation that is more economical than the traditional Vlasov formulation and is in explicitly canonical form. I show how this formulation can be used for simulating non-equilibrium dynamics in the Abelian Higgs model.

hep-lat↗

arXiv1999

Simulating hot Abelian gauge dynamics

The time evolution of soft modes in a quantum gauge field theory is to first approximation classical, but the equations of motion are non-local. We show how they can be written in a local and Hamiltonian way in an Abelian theory, and that this formulation is particularly suitable for numerical simulations. This makes it possible to simulate numerically non-equilibrium processes such as the phase transition in the Abelian Higgs model and and to study, for instance, bubble nucleation and defect formation. Such simulations would also help to understand phase transitions in more complicated gauge theories. Moreover, we show that the existing analytical results for the time-evolution in a pure-gauge theory correspond to a special class of initial conditions and that different initial conditions can lead to qualitatively different behavior. We compare the results of the simulations to analytical calculations and find an excellent agreement.

hep-ph↗

arXiv1998

The Phase Diagram of Three-Dimensional SU(3) + Adjoint Higgs Theory

We study the phase diagram of the three-dimensional SU(3)+adjoint Higgs theory with lattice Monte Carlo simulations. A critical line consisting of a first order line, a tricritical point and a second order line, divides the phase diagram into two parts distinguished by =0 and /=0. The location and the type of the critical line are determined by measuring the condensates and , and the masses of scalar and vector excitations. Although in principle there can be different types of broken phases, corresponding perturbatively to unbroken SU(2)xU(1) or U(1)xU(1) symmetries, we find that dynamically only the broken phase with SU(2)xU(1)-like properties is realized. The relation of the phase diagram to 4d finite temperature QCD is discussed.

hep-lat↗

arXiv1998

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

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 high-temperature 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.

hep-ph↗

arXiv1998

Gauge-invariant strings in the 3d U(1)+Higgs theory

We describe how the strings, which are classical solutions of the continuum three-dimensional U(1)+Higgs theory, can be studied on the lattice. The effect of an external magnetic field is also discussed and the first results on the string free energy are presented. It is shown that the string free energy can be used as an order parameter when the scalar self-coupling is large and the transition is continuous.

hep-lat↗

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

Vortices and the Ginzburg-Landau phase transition

The methods for studying the role of vortex loops in the phase transition of the Ginzburg-Landau theory of superconductivity using lattice Monte Carlo simulations are discussed. Gauge-invariant observables that measure the properties of the vortex loop distribution are defined. The exact relations between the lattice and continuum quantities make it possible to extrapolate the results of the simulations to the continuum limit. The relationship between spontaneous symmetry breaking and phase transitions is also reviewed, with an emphasis on the fact that a local symmetry cannot be broken.

cond-mat↗

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

High-T QCD and dimensional reduction: measuring the Debye mass

We study the high-temperature phase of SU(2) and SU(3) QCD using lattice simulations of an effective 3-dimensional SU(N) + adjoint Higgs -theory, obtained through dimensional reduction. We investigate the phase diagram of the 3D theory, and find that the high-T QCD phase corresponds to the metastable symmetric phase of the 3D theory. We measure the Debye screening mass m_D with gauge invariant operators; in particular we determine the O(g^2) and O(g^3) corrections to m_D. The corrections are seen to be large, modifying the standard power-counting hierarchy in high temperature QCD.

hep-lat↗

arXiv1997

Non-perturbative Debye mass in finite T QCD

Employing a non-perturbative gauge invariant definition of the Debye screening mass m_D in the effective field theory approach to finite T QCD, we use 3d lattice simulations to determine the leading O(g^2) and to estimate the next-to-leading O(g^3) corrections to m_D in the high temperature region. The O(g^2) correction is large and modifies qualitatively the standard power-counting hierarchy picture of correlation lengths in high temperature QCD.

hep-ph↗

arXiv1997

Lattice-continuum relations for 3d SU(N)+Higgs theories

3d lattice studies have recently attracted a lot of attention, especially in connection with finite temperature field theories. One ingredient in these studies is a perturbative computation of the 2-loop lattice counterterms, which are exact in the continuum limit. We extend previous such results to SU(N) gauge theories with Higgs fields in the fundamental and adjoint representations. The fundamental SU(3)xSU(2) case might be relevant for the electroweak phase transition in the MSSM, and the adjoint case for the GUT phase transition and for QCD in the high temperature phase. We also revisit the standard SU(2)xU(1) and U(1) theories.

hep-lat↗