Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang–Mills theory using the small flow-time expansion method

Abstract

We study latent heat and the pressure gap between the hot and cold phases at the first-order deconfining phase transition temperature of the SU(3) Yang–Mills theory. Performing simulations on lattices with various spatial volumes and lattice spacings, we calculate the gaps of the energy density and pressure using the small flow-time expansion (SF$t$X) method. We find that the latent heat $\Delta \epsilon$ in the continuum limit is $\Delta \epsilon /T^4 = 1.117 \pm 0.040$ for the aspect ratio $N_s/N_t=8$ and $1.349 \pm 0.038$ for $N_s/N_t=6$ at the transition temperature $T=T_c$. We also confirm that the pressure gap is consistent with zero, as expected from the dynamical balance of two phases at $T_c$. From hysteresis curves of the energy density near $T_c$, we show that the energy density in the (metastable) deconfined phase is sensitive to the spatial volume, while that in the confined phase is insensitive. Furthermore, we examine the effect of alternative procedures in the SF$t$X method—the order of the continuum and the vanishing flow-time extrapolations, and also the renormalization scale and higher-order corrections in the matching coefficients. We confirm that the final results are all very consistent with each other for these alternatives.

The upper right corner of the Columbia plot with staggered fermions

“…In contrast to that, for infinite heavy quark masses, QCD exhibits a first order thermal transition due to the spontaneous breaking of the global Z 3 center symmetry. The corresponding latent heat was calculated recently in the continuum limit [2,3]. Several approaches to study criticality in QCD in the heavy mass region, such as the derivative method, flow time expansion, reweighting from quenched QCD, the hopping parameter expansion or effective actions including the Polyakov loop term have been used and combined [2][3][4][5][6].…”

“…The corresponding latent heat was calculated recently in the continuum limit [2,3]. Several approaches to study criticality in QCD in the heavy mass region, such as the derivative method, flow time expansion, reweighting from quenched QCD, the hopping parameter expansion or effective actions including the Polyakov loop term have been used and combined [2][3][4][5][6]. Important results are the critical hopping parameter 𝜆 𝑐 and the latent heat or the energy gap (quenched QCD), clearly indicating a first order phase transition.…”

Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method

“…See Ref. [15] for our criterion to choose an optimum window. We confirm that the results are consistent within statistical errors under a variation of fitting windows.…”

“…In this study, we adopt the SF𝑡X method to calculate the latent heat Δ𝜖 and pressure gap Δ𝑝 at the first order phase transition of the SU(3) Yang-Mills theory [15]. Performing simulations at several lattice spacings and spatial volumes, we carry out the continuum extrapolation 𝑎 → 0 and study the finite volume effect.…”

“…Near the first order transition point, we separate the configurations into the hot (deconfined) and cold (confined) phases using the spatially averaged Polyakov loop Ω. See [15] for details. After the phase separation, we carry out the gradient flow on each of the configurations to measure flowed operators.…”