Finite-temperature Sp(4) Yang-Mills theory: towards the continuum

Abstract

We present numerical results obtained in a finite-temperature study of the Sp(4) Yang-Mills theory on the lattice. We study its first-order confinement/deconfinement phase transition, by reconstructing the density of states via the Logarithmic Linear Relaxation (LLR) algorithm. We perform our measurements on lattices with different extents of space and time (and aspect ratios). We estimate the size of discretisation and finite-volume artefacts. We find clear signatures of a first-order transition. We determine the critical coupling, the specific heat, and the surface tension, for finite extents of the thermal circle, and use the results to set bounds for the continuum theory.

Figures (3)

• Figure 1: Left panel: final result for $a_n$ as a function of the average plaquette, $u_p$, evaluated at the centre of the intervals, for fixed choice of lattice volume, and by varying the number of energy intervals. Right panel: final results for $a_n$ as a function of the average plaquette, $u_p$, evaluated at the centre of the intervals, for all spatial volumes considered, with fixed $N_t=5$.
• Figure 2: Left panel: probability distribution, $P_\beta(u_p)$, against the central value of the average plaquette. The inverse gauge coupling, $\beta$, has been tuned such that the maxima are of equal height. Right panel: surface tension term, $\tilde{I}$, extracted at finite volume, according to Eq. \ref{['eq:surface_tension']}.
• Figure 3: Left panel: specific heat, $C_V$, as a function of $\beta$. Middle panel: Binder cumulant, $B_V$, as a function of $\beta$. In both case, the position of the extrema yields a determination of the critical coupling. Right panel: comparison between inverse critical coupling, $\beta_c$, as determined from the plaquette distribution ($P$), the specific heat ($C_V$), and the Binder cumulant ($B_V$).