Themodynamics for pure SU($2$) gauge theory using gradient flow

TL;DR

This paper investigates the thermodynamics of pure SU(2) gauge theory using lattice Monte Carlo simulations and introduces a new reference scale based on the gradient flow method.

Contribution

It proposes a new reference scale $t_0$ for SU(2) gauge theory and applies the gradient flow to determine thermodynamic quantities from the energy-momentum tensor.

Findings

Established a scale $t_0$ for SU(2) gauge theory.

Computed thermodynamic quantities as functions of $T/T_c$.

Validated the use of gradient flow for thermodynamic analysis.

Abstract

We study the equation of state of pure SU($2$) gauge theory using Monte Carlo simulations. The scale-setting of lattice parameters has been carried by using the gradient flow. We propose a reference scale $t_0$ for the SU($2$) gauge theory satisfying $t^2 \langle E \rangle|_{t=t_0} =0.1$, which is fixed by a natural scaling-down of the standard $t_0$-scale for the SU($3$) case based on perturbative analyses. We also show the thermodynamic quantities as a function of $T/T_c$, which are derived by the energy-momentum tensor using the small flow-time expansion of the gradient flow.