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# Thermodynamics for pure SU(2) gauge theory using gradient flow

## Hirakida, T; Itou, E; Kouno, H

### Progress of theoretical and experimental physics. Volume 2019:Number 3 (2019, March 17th) -- Oxford University Press on behalf of the Physical Society of Japan

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• Title:
Thermodynamics for pure SU(2) gauge theory using gradient flow
• Author: Hirakida, T;
Itou, E;
Kouno, H
• Found In: Progress of theoretical and experimental physics. Volume 2019:Number 3 (2019, March 17th)
• Journal Title: Progress of theoretical and experimental physics
• Subjects: Mathematical physics--Periodicals; Physics--Periodicals; Dewey: 530.05
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$T/T_{\rm c}$, which are derived by the energy–momentum tensor using the small-flow-time expansion of the gradient flow.