Phase Transition In SU Research Articles

Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions

We suggest the possibility that the two-dimensional SU(2)$_k$ Wess-Zumino-Witten (WZW) theory, which has global SO(4) symmetry, can be continued to $2+\epsilon$ dimensions by enlarging the symmetry to SO$(4+\epsilon)$. This is motivated by the three-dimensional sigma model with SO(5) symmetry and a WZW term, which is relevant to deconfined criticality. If such a continuation exists, the structure of the renormalization group flows at small $\epsilon$ may be fixed by assuming analyticity in $\epsilon$. This leads to the conjecture that the WZW fixed point annihilates with a new, unstable fixed point at a critical dimensionality $d_c>2$. We suggest that $d_c < 3$ for all $k$, and we compute $d_c$ in the limit of large $k$. The flows support the conjecture that the deconfined phase transition in SU(2) magnets is a ``pseudocritical'' point with approximate SO(5), controlled by a fixed point slightly outside the physical parameter space.

Study of the Confinement/Deconfinement Phase Transition in Rotating Lattice SU(3) Gluodynamics

The effect of rotation on the confinement/deconfinement phase transition in SU(3) gluodynamics has been studied in lattice simulation in the rotating reference frame, where rotation is specified by an external gravitational field. To analyze the confinement/deconfinement phase transition, the Polyakov loop and its susceptibility have been calculated for various temperatures and angular velocities. The results obtained have indicated that the critical temperature of the confinement/deconfinement phase transition in SU(3) gluodynamics increases with the angular velocity.

On the first-order phase transition in SU(N) matrix models

Phase transition in SU(N) symmetric models for the adjoint field φ in the case of arbitrary N is investigated. We examine the fluctuation-induced symmetry breaking from the point of view of the ferromagnetic phase transition in the large spin Fermi system, where the order parameter 〈φ〉 occurs discontinuously for N≥4. The free energies of the systems are analyzed within both ε-expansion and the functional renormalization group.

Confinement/deconfinement phase transition in SU (3) Yang–Mills theory in view of dual superconductivity

In the preceeding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we discuss the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. We investigate chromomagnetic monopole currents induced by chromoelectric flux in both confinement and deconfinement phase by the numerical simulations on a lattice at finite temperature, and discuss the role of the chromomagnetic monopole in the confinement/deconfinement phase transition.

Geometrical clusterization and deconfinement phase transition in SU(2) gluodynamics

A novel approach to identify the geometrical (anti)clusters formed by the Polyakov loops of the same sign and to study their properties in the lattice SU(2) gluodynamics is developed. The (anti)cluster size distributions are analyzed for the lattice coupling constant β ∈ 2 [2:3115; 3]. The found distributions are similar to the ones existing in 2- and 3-dimensional Ising systems. Using the suggested approach, we explain the phase transition in SU(2) gluodynamics at β = 2.52 as a transition between two liquids during which one of the liquid droplets (the largest cluster of a certain Polyakov loop sign) experiences a condensation, while another droplet (the next to the largest cluster of opposite Polyakov loop sign) evaporates. The clusters of smaller sizes form two accompanying gases, which behave oppositely to their liquids. The liquid drop formula is used to analyze the distributions of the gas (anti)clusters and to determine their bulk, surface and topological parts of free energy. Surprisingly, even the monomer multiplicities are reproduced with high quality within such an approach. The behavior of surface tension of gaseous (anti)clusters is studied. It is shown that this quantity can serve as an order parameter of the deconfinement phase transition in SU(2) gluodynamics. Moreover, the critical exponent β of surface tension coefficient of gaseous clusters is found in the upper vicinity of critical temperature. Its value coincides with the one found for 3-dimensional Ising model within error bars. The Fisher topological exponent τ of (anti)clusters is found to have the same value 1:806±0:008, which agrees with an exactly solvable model of the nuclear liquid-gas phase transition and disagrees with the Fisher droplet model, which may evidence for the fact that the SU(2) gluodynamics and the model are in the same universality class.

Geometrical clusterization of Polyakjov loops in SU(2) lattice gluodynamics

The liquid droplet formula is applied to an analysis of the properties of geometrical (anti)clusters formed in SU(2) gluodynamics by the Polyakov loops of the same sign. Using this approach, we explain the phase transition in SU(2) gluodynamics as a transition between two liquids during which one of the liquid droplets (the largest cluster of a certain Polyakov loop sign) experiences a condensation, while the droplet of another liquid (the next to the largest cluster of the opposite sign of Polyakov loop) evaporates. The clusters of smaller sizes form two accompanying gases, which behave oppositely to their liquids. The liquid droplet formula is used to analyze the size distributions of the gas (anti)clusters. The fit of these distributions allows us to extract the temperature dependence of surface tension and the value of Fisher topological exponent τ for both kinds of gaseous clusters. It is shown that the surface tension coefficient of gaseous (anti)clusters can serve as an order parameter of the deconfinement phase transition in SU(2) gluodynamics. The Fisher topological exponent τ of (anti)clusters is found to have the same value 1.806 ± 0.008. This value disagrees with the famous Fisher droplet model, but it agrees well with an exactly solvable model of the nuclear liquid-gas phase transition. This finding may evidence for the fact that the SU(2) gluodynamics and this exactly solvable model of nuclear liquid-gas phase transition are in the same universality class.

Gluon dynamics, center symmetry, and the deconfinement phase transition in SU(3) pure Yang-Mills theory

The correlations between the modulus of the Polyakov loop, its phase $\ensuremath{\theta}$, and the Landau gauge gluon propagator at finite temperature are investigated in connection with the center symmetry for pure Yang-Mills SU(3) theory. In the deconfined phase, where the center symmetry is spontaneously broken, the phase of the Polyakov loop per configuration is close to $\ensuremath{\theta}=0$, $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}/3$. We find that the gluon propagator form factors associated with $\ensuremath{\theta}\ensuremath{\approx}0$ differ quantitatively and qualitatively from those associated to $\ensuremath{\theta}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}/3$. This difference between the form factors is a property of the deconfined phase and a sign of the spontaneous breaking of the center symmetry. Furthermore, given that this difference vanishes in the confined phase, it can be used as an order parameter associated to the deconfinement transition. For simulations near the critical temperature ${T}_{c}$, the difference between the propagators associated to $\ensuremath{\theta}\ensuremath{\approx}0$ and $\ensuremath{\theta}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}/3$ allows one to classify the configurations as belonging to the confined or deconfined phase. This establishes a selection procedure which has a measurable impact on the gluon form factors. Our results also show that the absence of the selection procedure can be erroneously interpreted as lattice artifacts.

Effective matrix model for deconfinement in pure gauge theories

We construct matrix models for the deconfining phase transition in SU(N) gauge theories, without dynamical quarks, at a nonzero temperature T. We generalize models with zero and one free parameter to study a model with two free parameters: besides perturbative terms ~T^4, we introduce terms ~T^2 and ~T^0. The two N-dependent parameters are determined by fitting to data from numerical simulations on the lattice for the pressure, including the latent heat. Good agreement is found for the pressure in the semi-quark gluon plasma (QGP), which is the region from Tc, the critical temperature, to about ~4 Tc. Above ~1.2 Tc, the pressure is a sum of a perturbative term, ~ +T^4, and a simple non-perturbative term, essentially just a constant times ~ -Tc^2 T^2. For the pressure, the details of the matrix model only enter within a very narrow window, from Tc to ~1.2 Tc, whose width does not change significantly with N. Without further adjustment, the model also agrees well with lattice data for the 't Hooft loop. This is notable, because in contrast to the pressure, the 't Hooft loop is sensitive to the details of the matrix model over the entire semi-QGP. For the (renormalized) Polyakov loop, though, our results disagree sharply with those from the lattice. Matrix models provide a natural and generic explanation for why the deconfining phase transition in SU(N) gauge theories is of first order not just for three, but also for four or more colors. Lastly, we consider gauge theories where there is no strict order parameter for deconfinement, such as for a G(2) gauge group. To agree with lattice measurements, in the G(2) matrix model it is essential to add terms which generate complete eigenvalue repulsion in the confining phase.

Quantifying zigzag motion of quarks

The quark condensate is calculated in terms of the effective string tension and the constituent quark mass. For 3 colors and 2 light flavors, the constituent mass is bounded from below by the value of 460 MeV. This value is only accessible when the string tension decreases linearly with the Schwinger proper time. For this reason, the Hausdorff dimension of a light-quark trajectory is equal to 4, indicating that these trajectories are similar to branched polymers, which can describe a weak first-order deconfinement phase transition in SU(3) Yang-Mills theory. Using this indication, we develop a gluon-chain model based on such trajectories.

Deconfined Criticality: Generic First-Order Transition in the SU(2) Symmetry Case

Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coupling is to a weak first-order transition, similar to the case of U(1) x U(1) symmetry. Our results imply that recent numeric studies of the Nèel antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.

Strongly First Order Chiral Phase Transition in SU(N_f)_L×SU(N_f)_R Sigma Model and Electroweak Baryogenesis

Strongly First Order Chiral Phase Transition in SU(N_f)_L×SU(N_f)_R Sigma Model and Electroweak Baryogenesis

Hedgehogs in Wilson loops and phase transition in SU(2) Yang–Mills theory

We suggest that the gauge-invariant hedgehog-like structures in the Wilson loops are physically interesting degrees of freedom in the Yang–Mills theory. The trajectories of these “hedgehog loops” are closed curves corresponding to center-valued (untraced) Wilson loops and are characterized by the center charge and winding number. We show numerically in the SU(2) Yang–Mills theory that the density of hedgehog structures in the thermal Wilson–Polyakov line is very sensitive to the finite-temperature phase transition. The (additively normalized) hedgehog line density behaves like an order parameter: The density is almost independent of the temperature in the confinement phase and changes substantially as the system enters the deconfinement phase. In particular, our results suggest that the (static) hedgehog lines may be relevant degrees of freedom around the deconfinement transition and thus affect evolution of the quark–gluon plasma in high-energy heavy-ion collisions.

Chiral phase structure of QCD with many flavors

We investigate QCD with a large number of massless flavors with the aid of renormalization group flow equations. We determine the critical number of flavors separating the phases with and without chiral symmetry breaking in SU(Nc) gauge theory with many fermion flavors. Our analysis includes all possible fermionic interaction channels in the pointlike four-fermion limit. Constraints from gauge invariance are resolved explicitly and regulator-scheme dependencies are studied. Our findings confirm the existence of an Nf window where the system is asymptotically free in the ultraviolet, but remains massless and chirally invariant on all scales, approaching a conformal fixed point in the infrared. Our prediction for the critical number of flavors of the zero-temperature chiral phase transition in SU(3) is Nf cr=10.0±0.29 (fermion)+1.55 -0.63 (gluon), with the errors arising from approximations in the fermionic and gluonic sectors, respectively.

Properties of the deconfining phase transition in SU(N) gauge theories

We extend our earlier investigation of the finite temperature deconfinement transition in SU(N) gauge theories, with the emphasis on what happens as N->oo. We calculate the latent heat in the continuum limit, and find the expected quadratic in N behaviour at large N. We confirm that the phase transition, which is second order for SU(2) and weakly first order for SU(3), becomes robustly first order for N>3 and strengthens as N increases. As an aside, we explain why the SU(2) specific heat shows no sign of any peak as T is varied across what is supposedly a second order phase transition. We calculate the effective string tension and electric gluon masses at T=Tc confirming the discontinuous nature of the transition for N>2. We explicitly show that the large-N `spatial' string tension does not vary with T for T Tc it increases as T-squared to a good approximation, and the k-string tension ratios closely satisfy Casimir Scaling. Within very small errors, we find a single Tc at which all the k-strings deconfine, i.e. a step-by-step breaking of the relevant centre symmetry does not occur. We calculate the interface tension but are unable to distinguish between linear or quadratic in N variations, each of which can lead to a striking but different N=oo deconfinement scenario. We remark on the location of the bulk phase transition, which bounds the range of our large-N calculations on the strong coupling side, and within whose hysteresis some of our larger-N calculations are performed.

Investigations on the deconfining phase transition in QCD

We investigate the deconfining phase transition in SU(3) pure gauge theory and in full QCD with two flavors of staggered fermions by means of a gauge invariant thermal partition functional. In the pure gauge case our finite size scaling analysis is in agreement with the well known weak first order phase transition. In the case of 2 flavors full QCD we find that the phase transition is consistent with weak first order, contrary to the expectation of a crossover for not too large quark masses.

Analysis of finite temperature phase transition using level spacing

Let B be the largest spacing between adjacent eigenvalues of the Polyakov loop. We propose to employ the distribution of B as an order parameter for the finite temperature phase transition in SU(N) lattice gauge theories. Using smeared links to reduce ultraviolet fluctuations, we carry out a test for the gauge group SU(3).

SU(N) gauge theories near Tc

We study the deconfinement phase transition in SU(N) gauge theories for $N$=2,3,4,6,8. The transition is first order for $N \ge 3$, with the strength increasing as $N$ increases. We extrapolate $T_c/\sqrt{\sigma}$ to the continuum limit for each $N$, and observe a rapid approach to the large $N$ limit. As $N$ increases the phase transition becomes clear-cut on smaller spatial volumes, indicating the absence of (non-singular) finite volume corrections at $N=\infty$ -- reminiscent of large $N$ reduction. The observed rapid increase of the inter-phase surface tension with $N$ may indicate that for $N=\infty$ the deconfinement transition cannot, in practise, occur.

The deconfining phase transition in full QCD with two dynamical flavors

We investigate the deconfining phase transition in SU(3) pure gauge theory and in full QCD with two flavors of staggered fermions. The phase transition is detected by measuring the free energy in presence of an abelian monopole background field. In the pure gauge case our finite size scaling analysis is in agreement with the well known presence of a weak first order phase transition. In the case of 2 flavors full QCD we find, using the standard pure gauge and staggered fermion actions, that the phase transition is consistent with weak first order, contrary to the expectation of a crossover for not too large quark masses and in agreement with results obtained by the Pisa group.

The high temperature phase transition in SU(N) gauge theories

We calculate the continuum value of the deconfining temperature in units of the string tension for SU(4), SU(6) and SU(8) gauge theories, and we recalculate its value for SU(2) and SU(3). We find that the $N$-dependence for $2 \leq N \leq 8$ is well fitted by $T_c/\sqrt{sigma} = 0.596(4) + 0.453(30)/N^2$, showing a rapid convergence to the large-N limit. We confirm our earlier result that the phase transition is first order for $N \geq 3$ and that it becomes stronger with increasing $N$. We also confirm that as $N$ increases the finite volume corrections become rapidly smaller and the phase transition becomes visible on ever smaller volumes. We interpret the latter as being due to the fact that the tension of the domain wall that separates the confining and deconfining phases increases rapidly with $N$. We speculate on the connection to Eguchi-Kawai reduction and to the idea of a Master Field.

Vortex critical behavior at the deconfinement phase transition

The de-confinement phase transition in SU(2) Yang-Mills theory is revisited in the vortex picture. Defining the world sheets of the confining vortices by maximal center projection, the percolation properties of the vortex lines in the hypercube consisting of the time axis and two spatial axis are studied. Using the percolation cumulant, the temperature for the percolation transition is seen to be in good agreement with the critical temperature of the thermal transition. The finite size scaling function for the cumulant is obtained. The critical index of the finite size scaling function is consistent with the index of the 3D Ising model.