Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1996-10-17
Phys.Rev.D56:151-160,1997
Physics
High Energy Physics
High Energy Physics - Lattice
32 pages of Latex, 13 PostScript figures. Replaced version containing extended finite size scaling analyses on $15^{3}\times3$
Scientific paper
10.1103/PhysRevD.56.151
We study the scaling properties of the static quark potential and the ratio of the critical temperature $T_c$ to the square root of the string tension $\sigma$ in the SU(3) pure gauge theory using a renormalization group improved action. We first determine the critical coupling $\beta_c$ on lattices with temporal extension $N_t=3$, 4, and 6, and then calculate the static quark potential at the critical couplings on lattices at zero temperature. We note that the static quark potentials obtained are rotationally invariant with errors of at most 1 - 2 % in all the three cases, and that the potential $V(R)$ in physical units scales in the whole region of $R$ investigated. The values of $T_{c}/\sqrt{\sigma}$ for the three cases in the infinite volume limit are identical within errors. We estimate the value in the continuum limit to be $T_{c}/\sqrt{\sigma} = 0.656(4)$, which is slightly larger than the value in the continuum limit from the one-plaquette action, 0.629(3).
Iwasaki Yoshihito
Kanaya Kazuyuki
Kaneko Tak
Yoshi'e T.
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