The Status of Lattice QCD at Finite Temperature

TL;DR

The article surveys the status of lattice QCD at finite temperature, detailing the phase diagram, equation of state, screening phenomena, and spectral properties, and extends to small baryon density using reweighting, Taylor expansion, and imaginary-chemical-potential methods. It shows that the deconfined quark–gluon plasma remains strongly coupled with significant non-perturbative effects, and that dimensional reduction provides a powerful framework for soft-mode physics above roughly $2T_c$. The work synthesizes results for the critical temperature, screening masses, quark-number susceptibilities, and static free energies, highlighting both successes (controlled pure-gauge results, qualitative dynamical insights) and current limitations (physical quark masses, continuum extrapolation, real-time dynamics, finite-density volume effects). Collectively, these findings connect lattice QCD predictions with heavy-ion phenomenology and early-universe physics, while outlining avenues to reach physical quark masses, larger volumes, and better control of systematic uncertainties.

Abstract

The status of lattice QCD investigations at high temperature is reviewed. After a short introduction into thermal QCD on the lattice we report on the present understanding of the phase diagram and the equation of state, in particular in presence of dynamical quarks. We continue with a discussion of various screening lengths in the plasma phase including results from dimensionally reduced QCD. This is followed by summarizing lattice data on quark number susceptibilities and spectral densities, both of which are of immediate relevance to the interpretation of heavy ion experiments. A major section is devoted to presenting simulations of QCD at small yet phenomenologically important values for the baryon density.

Figures (13)

• Figure 1: The phase diagram, expected (left) and lattice data (right), in the plane of strange and degenerate u,d quark masses.
• Figure 2: Left: $T_c$ in units of the vector meson mass for $N_f=2$, for a variety of improved actions Peikertmilc_tcjapan_tcUrs_tcdwf_tc. Right: $N_f=2,3$ for improved (p4) staggered quarks, compared to $N_f=2$ standard (std) simulations Peikert.
• Figure 3: Left: flavor dependence of the pressure for $N_t=4$ lattices compared to a continuum extrapolated pure gauge result Peikert_eos. Right: energy density for $N_f=2$ improved Wilson quarks on $N_t=4$ (filled symbols) and $N_t = 6$ (open symbols) Wilson_eos. Marks on the right side denote Stefan-Boltzmann limits.
• Figure 4: The pressure of pure gauge theory from dimensional reduction, with an as yet undetermined constant $e_0$. From 3pres.
• Figure 5: Left: Screening masses for the pure gauge theory, corresponding to the continuum $0^{++}_+$ (circles) and $0^{+-}_-$ (squares) channels. From dg2. Right: Mesonic screening masses in the quenched chiral limit. Below $T_c$, $M_{\rho}/T_c$PSchmidtBinew is plotted, the line denotes the $T=0$ value. Open Wilson symbols denote anisotropic lattices Nucu_1. Staggered pion data are extrapolated to $a=0$Sourendu2, Wilson and staggered rho are from $N_t=8$PSchmidt and 16 Binew lattices. The free quark limit has not been corrected for finite volume effects.