Glauber dynamics of phase transitions: SU(3) lattice gauge theory

Motivated by questions about the QCD deconfining phase transition, we studied in two previous papers model A (Glauber) dynamics of 2D and 3D Potts models, focusing on structure factor evolution under heating (heating in the gauge theory notation, i.e., cooling of the spin systems). In the present paper we set for 3D Potts models (Ising and 3-state) the scale of the dynamical effects by comparing to equilibrium results at first and second order phase transition temperatures, obtained by reweighting from a multicanonical ensemble. Our finding is that the dynamics entirely overwhelms the critical and noncritical equilibrium effects. In the second half of the paper we extend our results by investigating the Glauber dynamics of pure SU(3) lattice gauge on $N_{\tau }{N}_{\sigma }^3$ lattices directly under heating quenches from the confined into the deconfined regime. The exponential growth factors of the initial response are calculated, which give Debye screening mass estimates. The quench leads to competing vacuum domains of distinct $Z_3$ triality, which delay equilibration of pure gauge theory forever, while their role in full QCD remains a subtle question. As in spin systems we find for pure SU(3) gauge theory a dynamical growth of structure factors, reaching maxima which scale approximately with the volume of the system, before settling down to equilibrium. Their influence on various observables is studied and different lattice sizes are simulated 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.

Figure 1

SFs $F_i,i=1,\dots ,9$ from simulations of the Ising model on an ${80}^3$ lattice.

Figure 2

Finite size behavior of SF $F_1$ from Ising model simulations on $L^3$ lattices.

Figure 3

Fit of the $F_1^{\max }$ maxima of Table  to the FSS form (16).

Figure 4

SFs $F_i,i=1,\dots ,9$ from simulations of the 3-state Potts model on a ${50}^3$ lattice.

Figure 5

Finite size behavior of SF $F_1$ from 3-state Potts model simulations on $L^3$ lattices.

Figure 6

Time evolution of SF $F_1$ for the 3-state Potts model on $L^3$ lattices after a quench from $\beta =0.2\to 0.3$.

Figure 7

Time evolution of SF $F_1$ for the 3-state Potts model on $L^3$ lattices after a quench from $\beta =0.2\to 0.28$.

Figure 8

Time positions of the SF $F_1$ maxima versus lattice size.

Figure 9

Time evolution of SFs $F_i,i=1,\dots ,4$ for the 3-state Potts model on a ${40}^3$ lattice after a quench below ${\beta }_c$ from $\beta =0.2\to 0.27$.

Figure 10

Time evolution of SF $F_1/V$ for SU(3) lattice gauge theory on $4\times N_{\sigma }^3$ lattices after a quench $6/g^2=5.5\to 5.92$.

Figure 11

Time evolution of SF $F_1/F_{1,f}$ for SU(3) lattice gauge theory on $N_{\tau }{N}_{\sigma }^3$ lattices of constant physical volume of a quench to $T_f/T_c=1.25$.

Figure 12

Time evolution of SF $F_1/F_{1,f}$ for SU(3) lattice gauge theory on $N_{\tau }{N}_{\sigma }^3$ lattices of constant physical volume of a quench to $T_f/T_c=1.568$.

Figure 13

SU(3) determination of $p_c$ for $T_f/T_c=1.25$.

Figure 14

SU(3) determination of $p_c$ for $T_f/T_c=1.568$.

Figure 15

Time dependence of Polyakov loop correlations $C_o(d)$ on the $8\times {32}^3$ lattice for $T_f/T_c=1.25$ and various $d$ values.

Figure 16

Falloff behavior of the Polyakov loop correlations of Fig. 15 at different times.

Figure 17

SU(3) gluonic energy density on the $4\times {16}^3$ lattice: (a) with $P_0$ calculated from the time series after the quench and (b) using equilibrium values for $P_0$.

Figure 18

SU(3) gluonic energy densities and pressures at $T_f/T_c=1.25$.