Thermodynamics of SU(3) gauge theory on anisotropic lattices

TL;DR

This study investigates the thermodynamics of SU(3) gauge theory at finite temperature using anisotropic lattices, achieving more accurate continuum results that align with previous isotropic lattice findings.

Contribution

It demonstrates that anisotropic lattices provide a reliable and improved method for calculating the equation of state in SU(3) gauge theory, with better control over continuum extrapolation.

Findings

Pressure and energy density satisfy leading $1/N_t^2$ scaling.

Continuum results agree with previous isotropic lattice studies.

Anisotropic lattices yield smaller, more reliable errors.

Abstract

Finite temperature SU(3) gauge theory is studied on anisotropic lattices using the standard plaquette gauge action. The equation of state is calculated on $16^{3} \times 8$, $20^{3} \times 10$ and $24^{3} \times 12$ lattices with the anisotropy $\xi \equiv a_s / a_t = 2$, where $a_s$ and $a_t$ are the spatial and temporal lattice spacings. Unlike the case of the isotropic lattice on which $N_t=4$ data deviate significantly from the leading scaling behavior, the pressure and energy density on an anisotropic lattice are found to satisfy well the leading $1/N_t^2$ scaling from our coarsest lattice, $N_t/\xi=4$. With three data points at $N_t/\xi=4$, 5 and 6, we perform a well controlled continuum extrapolation of the equation of state. Our results in the continuum limit agree with a previous result from isotropic lattices using the same action, but have smaller and more reliable errors.