A new computation of the correlation length near the deconfining transition in SU(3 (original) (raw)

Correlation length and order of the deconfining phase transition

Physical Review Letters, 1989

We analyze SU(2) and SU(3) lattice gauge theory on L, XL2~l attices (L,~L) By P,. we denote the critical coupling at L =~. In the neighborhood of the deconfining phase transition, at appropriately defined coupling constants p(L, L'), L & L' [with p(L, L') p, for L'~] , the correlation length g scales-L/L' for secondand first order transitions (g =1/Ei with Ei the energy of one unit of 't Hooft electric fiux). Linearization around the couplings P(L, L') allows the calculation of critical exponents. Numerical results (L, =4) support a second-order transition for SU(2), but not for SU(3).

Nature of the Deconfining Phase Transition in SU(3) Lattice Gauge Theory

Physical Review Letters, 1988

Monte Carlo calculations on lattices with large spatial volume show that the SU(3) deconfining phase transition is more weakly first order than previously thought. We have studied the transition for NT 4 and 6 on lattices of spatial volumes 16', 20, and 24. The 24 x4 calculations show a sharp first-order phase transition, yielding a latent heat AC/T of 2.54~0. 12. The 24'&6 calculations suffer greater finite-volume smearing, hut suggest that d, C/T4 2.48~0.24. Correlation lengths increase significantly near the transition, and the energy plus pressure of the ordered phase depends strongly on P.

The SU(3) deconfining phase transition with Symanzik action

Physics Letters B, 1994

We report on the determination of the deconfining temperature in SU (3) pure gauge theory, using the Symanzik tree level improved action, on lattices of size 3 × 12 3 , 4 × 16 3 , 5 × 20 3 , 6 × 24 3 . We find that the asymptotic scaling violation pattern is similar to the one observed using the Wilson action. We conclude that the irrelevant operators do not affect, in the range of couplings considered, the lattice β function. An analysis based on an effective coupling formulation shows an apparent improvement.

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

2005

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 TTc 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.

Non-equilibrium signals of the SU(3) deconfining phase transition

Proceedings of XXIVth International Symposium on Lattice Field Theory — PoS(LAT2006), 2006

In SU(3) simulations with the model A (Glauber) dynamics we find unambiguous signal for the transition when the (driving) temperature T f is larger than T c. A dynamical growth of Polyakov loop structure factors, reaching maxima which scale approximately with the volume of the system, precedes equilibration. We study their influence on various observables, using different lattice sizes to illustrate an approach to a finite volume continuum limit. Strong correlations are found during the dynamical process, but not in the deconfined phase at equilibrium. Debye screening masses m D (T f) are estimated from initial response to the temperature change and found to be consistent with equilibrium estimates by Kaczmarek et al.

Toward an analytic determination of the deconfinement temperature in SU(2) lattice gauge theory

Nuclear Physics B, 1996

We consider the SU(2) lattice gauge theory at finite temperature in (d+1) dimensions, with different couplings β t and β s for timelike and spacelike plaquettes. By using the character expansion of the Wilson action and performing the integrals over space-like link variables, we find an effective action for the Polyakov loops which is exact to all orders in β t and to the first nontrivial order in β s . The critical coupling for the deconfinement transition is determined in the (3+1) dimensional case, by the mean field method, for different values of the lattice size N t in the compactified time direction and of the asymmetry parameter ρ = β t /β s . We find good agreement with Montecarlo simulations in the range 1 ≤ N t ≤ 5, and good qualitative agreement in the same range with the logarithmic scaling law of QCD. Moreover the dependence of the results from the parameter ρ is in excellent agreement with previous theoretical predictions.

The deconfining phase transition in SU (< i> Nc) gauge theories

Nuclear Physics B-Proceedings Supplements, 2003

We report on our ongoing investigation of the deconfining phase transition in SU(4) and SU(6) gauge theories. We calculate the critical couplings while taking care to avoid the influence of a nearby bulk phase transition. We determine the latent heat of the phase transition and investigate the order and the strength of the transition at large Nc. We also report on our determination of the critical temperature expressed in units of the string tension in the large Nc limit.

On the order of SU(2) deconfinement transition

We examine certain issues related to the universality of the SU(2) lattice gauge theory at non-zero temperatures. Using Monte Carlo simulations and strong coupling expansions, we study the behavior of the deconfinement transition in an extended coupling plane (β, β A ) around the tricritical point where the deconfinement transition changes from second to first order. Our numerical results on N τ =2,4,6,8 lattices show that the tricritical point first moves down towards the Wilson axis and and then moves slowly upwards, if at all, as the lattice spacing is reduced. Lattices with very large N τ seem to be therefore necessary for the mixed action to exhibit the critical exponents of

SU(3) deconfining phase transition with finite volume corrections due to a confined exterior

Physical Review D, 2013

Using the geometry of a double-layered torus we investigate the deconfining phase transition of pure SU(3) lattice gauge theory by Markov chain Monte Carlo simulations. In one layer, called "outside", the temperature is set below the deconfining temperature and in the other, called "inside", it is iterated to a pseudo-transition temperature. Lattice sizes are chosen in a range suggested by the physical volumes achieved in relativistic heavy ion collisions and both temperatures are kept close enough to stay in the SU(3) scaling region, which is required for approaching a quantum continuum limit. Properties of the transition are studied as function of the volume for three outside temperatures. When compared with infinite volume extrapolations, small volume corrections of the deconfining temperature and width compete with those found by including quarks. Effective finite size scaling exponents of the specific heat and Polyakov loop susceptibilities are also calculated.

Universality and the deconfinement phase transition in SU(2) lattice gauge theory

Nuclear Physics B, 1995

We study the three dimensional fundamental-adjoint SU(2) lattice gauge theory at non-zero temperatures by Monte Carlo simulations. On an 8 3 × 2 lattice, at β A = 1.1, where β A is the adjoint coupling, we find no evidence of any transition at the location of a previously known bulk phase transition around β = 1.33. Moreover, the deconfinement transition at β A = 1.1 occurs at β = 1.20 and is of first order for β A ≥ 1.1, thus implying a change of universality class from that of the Wilson action at β A = 0. Computations of the plaquette susceptibility and the temporal and spatial Polyakov loops on 8 3 × 4 and 16 3 × 8 lattices at β A = 1.1 further support these conclusions and suggest that the previously claimed bulk transition around β = 1.33 is, in fact, the first order deconfinement transition. Simulations at larger β A and the measurements of the mass gaps from the correlation functions of temporal and spatial Polyakov loops also confirm the temperature dependent nature of the above transition. The consequences of our results on universality are discussed.

2 Spectral Density Study of the SU(3) Deconfining Phase Transition†

2016

We present spectral density reweighting techniques adapted to the analysis of a time series of data with a continuous range of allowed values. In a first application we analyze action and Polyakov line data from a Monte Carlo simulation on L t L 3 (L t = 2, 4) lattices for the SU(3) deconfining phase transition. We calculate partition function zeros, as well as maxima of the specific heat and of the order parameter susceptibility. Details and warnings are given concerning i) autocorrelations in computer time and ii) a reliable extraction of partition function †

Spectral density study of the SU(3) deconfining phase transition

Nuclear Physics B, 1992

The deconfinement transition in SU(2) lattice gauge theory

Nuclear Physics B - Proceedings Supplements, 1995

The deconfinement transition in SU(4) lattice gauge theory is investigated on N 3 s × N t lattices for N s = 8-16 and N t = 4-8 using a modified Wilson action which is expected to be free of any bulk transitions. The susceptibility χ max |L| , where L is the order parameter for deconfinement, is found to increase linearly with spatial volume for N t = 4, 5, and 6, indicating a first order deconfinement phase transition. The latent heat of the transition is estimated to be ≈ 2 3 of the corresponding ideal gas energy density at T c .

Scaling, asymptotic scaling, and Symanzik improvement: Deconfinement temperature in SU(2) pure gauge theory

Physical Review D, 1994

We report on a high statistics simulation of SU(2) pure gauge field theory at finite temperature, using Symanzik action. We determine the critical coupling for the deconfinement phase transition on lattices up to 8 x 24, using Finite Size Scaling techniques. We find that the pattern of asymptotic scaling violation is essentially the same as the one observed with conventional, not improved action. On the other hand, the use of effective couplings defined in terms of plaquette expectation values shows a precocious scaling, with respect to an analogous analysis of data obtained by the use of Wilson action, which we interpret as an effect of improvement.

Thermalization in SU(3) gauge theory after a deconfining quench

Physical Review D, 2008

We determine the time evolution of fluctuations of the Polyakov loop after a quench into the deconfined phase of SU(3) gauge theory from a simple classical relativistic Lagrangian. We compare the structure factors, which indicate spinodal decomposition followed by relaxation, to those obtained via Markov Chain Monte Carlo techniques in SU(3) lattice gauge theory. We find that the time when the structure factor peaks diverges like ∼ 1/k 2 in the long-wavelength limit. This is due to formation of competing Z(3) domains for configurations where the Polyakov loop exhibits non-perturbatively large variations in space, which delay thermalization of long wavelength modes. For realistic temperatures, and away from the extreme weak-coupling limit, we find that even modes with k on the order of T experience delayed thermalization. Relaxation times of very long wavelength modes are found to be on the order of the size of the system; thus, the dynamics of competing domains should accompany the hydrodynamic description of the deconfined vacuum.

External field dependence of deconfinement temperature in SU(3)

Nuclear Physics B - Proceedings Supplements, 2002

We study vacuum dynamics of SU(3) lattice gauge theory at finite temperature. Using the lattice Schr5dinger functional, SU(3) vacuum is probed by means of an external constant Abelian chromomagnetic field. Our preliminary numerical data suggest that, by increasing the strength of the applied external field, deconfinement temperature decreases towards zero. This means that strong enough Abelian chromomagnetic fields destroy confinement of color.

The deconfinement transition in SU(4) lattice gauge theory

Nuclear Physics B - Proceedings Supplements, 2002

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

2003

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 NNN-dependence for 2leqNleq82 \leq N \leq 82leqNleq8 is well fitted by Tc/sqrtsigma=0.596(4)+0.453(30)/N2T_c/\sqrt{sigma} = 0.596(4) + 0.453(30)/N^2Tc/sqrtsigma=0.596(4)+0.453(30)/N2, showing a rapid convergence to the large-N limit. We confirm our earlier result that the phase transition is first order for Ngeq3N \geq 3Ngeq3 and that it becomes stronger with increasing NNN. We also confirm that as NNN 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 NNN. We speculate on the connection to Eguchi-Kawai reduction and to the idea of a Master Field.