Finite Temperature Deconfinement Phase Transition Research Articles

Confinement and the center of the gauge group

The question of the role of the center of the gauge group in the phenomenon of confinement in Yang-Mills theory is addressed. The investigation is performed from the most general perspective of considering all possible choices for the gauge symmetry group. In this context, an interesting role is played by G(2) Yang-Mills theory: the simplest pure gauge theory with a trivial center and without 't Hooft flux vortices. Numerical simulations show the presence of a first order finite temperature deconfinement phase transition in G(2) Yang-Mills theory in (3+1) dimensions. Interestingly, the G(2) gauge symmetry can be broken to an SU(3) subgroup by the Higgs mechanism. We investigate the relation between the deconfinement phase transition in G(2) and SU(3) Yang-Mills theories by numerical simulations in the G(2) gauge-Higgs system.

Another weak first order deconfinement transition: three-dimensionalSU(5) gauge theory

We examine the finite-temperature deconfinement phase transition of (2+1)-dimensional SU(5) Yang-Mills theory via non-perturbative lattice simulations. Unsurprisingly, we find that the transition is of first order, however it appears to be weak. This fits naturally into the general picture of "large" gauge groups having a first order deconfinement transition, even when the center symmetry associated with the transition might suggest otherwise.

A cluster algorithm for lattice gauge theories

A new algorithm for simulating compact U(1) lattice gauge theory in three dimensions is presented which is based on global changes in the configuration space. We show that this algorithm provides an effective way to extract partition functions at given external flux. As an application, we study numerically the finite temperature deconfinement phase transition.

Center vortex model for the infrared sector of SU(3) Yang–Mills theory—confinement and deconfinement

The center vortex model for the infrared sector of Yang–Mills theory, previously studied for the SU(2) gauge group, is extended to SU(3). This model is based on the assumption that vortex world-surfaces can be viewed as random surfaces in Euclidean space–time. The confining properties are investigated, with a particular emphasis on the finite-temperature deconfining phase transition. The model predicts a very weak first order transition, in agreement with SU(3) lattice Yang–Mills theory, and also reproduces a consistent behavior of the spatial string tension in the deconfined phase. The geometrical structure of the center vortices is studied, including vortex branchings, which are a new property of the SU(3) case.

Fundamental matter and the deconfining phase transition in 2+1 D

We analyze the effect of heavy fundamentally charged particles on the finite temperature deconfining phase transition in the (2+1)-dimensional Georgi–Glashow model. We show that in the presence of fundamental matter the transition turns into a crossover. The near critical theory is mapped onto the 2-dimensional Ising model in an external magnetic field. Using this mapping we determine the width of the crossover region as well as the specific heat as a function of the fundamental mass.

Deconfining phase transition in the 3D Georgi–Glashow model with finite Higgs-boson mass

The (2+1)D Georgi–Glashow model is explored at finite temperature in the regime when the Higgs boson is not infinitely heavy. The resulting Higgs-mediated interaction of monopoles leads to the appearance of a certain upper bound for the parameter of the weak-coupling approximation. Namely, when this bound is exceeded, the cumulant expansion used for the average over the Higgs field breaks down. The finite-temperature deconfining phase transition with the account for the same Higgs-mediated interaction of monopoles is further analysed. It is demonstrated that in the general case, accounting for this interaction leads to the existence of two distinct phase transitions separated by the temperature region where W-bosons exist in both, molecular and plasma, phases. The dependence of possible ranges of the critical temperatures corresponding to these phase transitions on the parameters of the Georgi–Glashow model is discussed. The difference in the RG behaviour of the fugacity of W-bosons from the respective behaviour of this quantity in the compact-QED limit of the model is finally pointed out.

Deconfining phase transition in 2+1 D: the Georgi-Glashow model

We analyze the finite temperature deconfining phase transition in 2+1 dimensional Georgi-Glashow model. We show explicitly that the transition is due to the restoration of the magnetic $Z_2$ symmetry and that it is in the Ising universality class. We find that neglecting effects of the charged $W$ bosons leads to incorrect predictions for the value of the critical temperature and the universality class of the transition, as well as for various correlation functions in the high temperature phase. We derive the effective action for the Polyakov loop in the high temperature phase and calculate the correlation functions of magnetic vortex operators.

Z2 monopoles, vortices and the universality of the SU(2) deconfinement transition

We investigate the effect of Z 2 magnetic monopoles and vortices on the finite temperature deconfinement phase transition in the fundamental - adjoint SU(2) lattice gauge theory. In the limit of complete suppression of the Z 2 monopoles, the mixed action for the SU(2) theory in its Villain form is shown to be self-dual under the exchange of the fundamental and adjoint couplings. By further suppressing the Z 2 vortices we show that the extended model reduces to the Wilson action with a modified coupling. The universality of the SU(2) deconfinement phase transition with the Ising model is therefore expected to remain intact in the entire plane of the fundamental-adjoint couplings in the continuum limit. The self-duality arguments related to the suppression of Z 2 monopoles are also applicable to the Villain form of mixed action for the SU( N) theory with Z N magnetic monopoles.

A quark-antiquark condensate in three-dimensional QCD

Three-dimensional lattice QCD is studied by Monte Carlo simulations within the quenched approximation. At zero temperature a quark-antiquark condensate is observed in the limit of vanishing quark masses. The condensate vanishes continuously at the finite-temperature deconfinement phase transition of the theory. A natural interpretation of this phenomenon in the full theory with dynamical quarks is in terms of the spontaneous flavor symmetry breaking U( N f )→ U( N f /2)× U( N f /2). In addition, the spectrum of low-lying Dirac operator eigenvalues is computed and found to be consistent with a flat distribution at zero temperature, in agreement with analytical predictions.

Disappearance of the Abrikosov vortex above the deconfining phase transition in SU(2) lattice gauge theory.

We calculate the solenoidal magnetic monopole current and electric flux distributions at finite temperature in the presence of a static quark antiquark pair. The simulation was performed using SU(2) lattice gauge theory in the maximal Abelian gauge. We find that the monopole current and electric flux distributions are quite different below and above the finite temperature deconfining phase transition point and agree with predictions of the Ginzburg-Landau effective theory.

Finite-temperature phase transition in SU(2) lattice gauge theory with extended action

We study the three dimensional fundamental-adjoint SU(2) lattice gauge theory at finite temperature by Monte Carlo simulations. We find that the finite-temperature deconfinement phase transition line joins the first-order bulk phase transition line at its endpoint. Moreover, across the bulk transition line, the Polyakov loop undergoes a discontinuous jump implying the existence of both confining and deconfining phases on its two sides. Implications for universality and the nature of the confining-deconfining transition are discussed.

Scaling and asymptotic scaling in the SU(2) gauge theory

We present results from a large volume study of the finite temperature deconfinement phase transition. The questions of scaling and asymptotic scaling are addressed. We find that an extrapolation of the critical temperature and the string tension to the continuum limit is possible when an effectivecoupling defined in terms of the plaquette operator is used.

Monopoles, gluons and the use of c-periodic lattice gauge fields

New C-periddic boundary, which are topologically different from periodic ones, are introduced to lattice gauge theory. When shifted by L lattice spacings C-periodic fields are replaced by their charge conjugates. In abelian lattice gauge theory C-periodic boundary conditions allow the existence of single charged particles (like monopoles) whereas periodic systems are always neutral. In nonabelian lattice gauge theory C-periodic boundary conditions affect the 't Hooft Z N flux sectors. For example, in the SU (3) case the flux sectors are entirely eliminated. This has interesting effects on the finite volume glueball mass spectrum and on the finite temperature deconfinement phase transition.

Critical behavior at the deconfinement phase transition of SU(2) lattice gauge theory in (2 + 1) dimensions

The finite-temperature deconfinement phase transition of SU(2) lattice gauge theory in (2 + 1) dimensions is studied by Monte Carlo methods. Comparison is made with the expected form of correlation functions on both sides of the critical point. The critical behavior is compared with expectations based on universality arguments. Attempts are made to extract unbiased values of critical exponents on several lattices sizes. The behavior of Polyakov loops in higher representations of the gauge group is studied close to the phase transition.

Order of the deconfining phase transition in SU(3) lattice gauge theory.

The nature of the finite-temperature deconfining phase transition is studied by Monte Carlo simulation on lattices ranging over 8{sup 3}{times}4 to 36{sup 3}{times}4. The spatial-volume dependence of the susceptibility and the mass gap strongly support a first-order transition. This is corroborated by an explicit construction of the effective {ital Z}(3) spin system whose dominant two-spin couplings are found to be all positive.

On the order of the finite temperature deconfinement phase transition in Z(2) and Z(3) lattice gauge theories

Using Monte Carlo methods, we show that the finite temperature deconfinement phase transition in Z(3) lattice gauge theory is of first order by presenting evidence for the coexistence of the two phases in the transition region. A similar study for the Z(2) theory, however, failed to yield any such evidence, thus indicating the corresponding transition to be of higher order.