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.

arXiv comment26 pages, 6 figures, 6 tables; minor corrections, a few precisions added

References in corpus (10)

• Thermodynamics of SU(3) Lattice Gauge Theory
• The QCD Equation of State with almost Physical Quark Masses
• Free Energy of QCD at High Temperature
• SU(N) gauge theories in 2+1 dimensions
• How to resum long-distance contributions to the QCD pressure?
• The closed string spectrum of SU(N) gauge theories in 2+1 dimensions
• High Temperature 3D QCD: Dimensional Reduction at Work
• Finite size analysis of the pseudo specific heat in SU(2) gauge theory
• 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 (19)

• Thermodynamics of the QCD plasma and the large-N limit
• SU(N) gauge theories at large N
• Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions II - The deconfined phase
• QCD thermodynamics from lattice calculations with non-equilibrium methods: The SU(3) equation of state
• 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
• Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
• Jarzynski's theorem for lattice gauge theory
• Exceptional thermodynamics: The equation of state of G(2) gauge theory
• Zero Point Energy of Renormalized Wilson Loops
• Universal signatures of the effective string in finite temperature lattice gauge theories
• Three dimensional finite temperature SU(3) gauge theory in the confined region and the string picture
• Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature
• Matrix model for deconfinement in an SU(2) gauge theory in 2+1 dimensions
• Three dimensional finite temperature SU(3) gauge theory near the phase transition
• Matrix model for deconfinement in a SU(Nc) gauge theory in 2+1 dimensions
• 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