Kavli Affiliate: Masahito Yamazaki
| First 5 Authors: Norikazu Yamada, Masahito Yamazaki, Ryuichiro Kitano, ,
| Summary:
We apply the previously-developed sub-volume method to study the
$theta$-dependence of the four-dimensional SU(2) Yang-Mills theory at finite
temperature. We calculate the first two coefficients, the topological
susceptibility $chi$ and the fourth cumulant $b_2$, in the $theta$-expansion
of the free energy density around the critical temperature ($T_c$) for the
confinement-deconfinement transition. Lattice calculations are performed with
three different spatial sizes $24^3,32^3,48^3$ to monitor finite size effects,
while the temporal size is fixed to be $8$. The systematic uncertainty
associated with the sub-volume extrapolation is studied with special care. The
sub-volume method allows us to determine the values of $b_2$ much more
accurately than the standard full-volume method, and we successfully identify
the temperature dependence of $b_2$ around $T_c$. Our numerical results suggest
that the $theta$-dependence of the free energy density near $theta=0$ changes
from $4chi(1-cos(theta/2))$ to $chi(1-costheta)$ as the temperature
crosses $T_c$.
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