Thermodynamics of SU(3) Gauge Theory in 2 + 1 Dimensions

Abstract

The pressure, and the energy and entropy densities are determined for the SU(3) gauge theory in $2+1$ dimensions from lattice Monte Carlo calculations in the interval $0.6\le T/T_c\le 15$. The finite temperature lattices simulated have temporal extent $N_{\tau }=2,4,6$ and 8, and spatial volumes $N_S^2$ such that the aspect ratio is $N_S/N_{\tau }=8$. To obtain the thermodynamical quantities, we calculate the averages of the temporal plaquettes $P_{\tau }$ and the spatial plaquettes $P_S$ on these lattices. We also need the zero temperature averages of the plaquettes $P_0$, calculated on symmetric lattices with $N_{\tau }=N_S$. We discuss in detail the finite size ($N_S$-dependent) effects. These disappear exponentially. For the zero temperature lattices we find that the coefficient of $N_S$ in the exponent is of the order of the glueball mass. On the finite temperature lattices it lies between the two lowest screening masses. For the aspect ratio equal to eight, the systematic errors coming from the finite size effects are much smaller than our statistical errors. We argue that in the continuum limit, at high enough temperature, the pressure can be parametrized by the very simple formula $p=a-b{T}_c/T$ where $a$ and $b$ are two constants. Using the thermodynamical identities for a large homogeneous system, this parametrization then determines the other thermodynamical variables in the same temperature range.

26 pages, 6 figures, 6 tables; minor corrections, a few precisions added

References in corpus (4)

• The QCD Equation of State with almost Physical Quark Masses
• The closed string spectrum of SU(N) gauge theories in 2+1 dimensions
• The equation of state at high temperatures from lattice QCD
• Towards 4-loop NSPT result for a 3-dimensional condensate-contribution to hot QCD pressure

Cited by in corpus (9)

• SU(N) gauge theories at large N
• Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions I - The confining phase
• Trace Anomaly, Thermal Power Corrections and Dimension Two condensates in the deconfined phase
• Exceptional thermodynamics: The equation of state of G(2) gauge theory
• Zero Point Energy of Renormalized Wilson Loops
• Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature
• Thermal power terms in the Einstein-dilaton system
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Quadratic thermal terms in the deconfined phase from holography