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We investigate the chiral transition of $U(3)$ lattice gauge theory based on
the strong coupling expansion. A generalized vertex model with vertices and
weights derived from the tensor network approach of the dual representation of
lattice QCD with staggered fermions is used and the configurations are sampled
by the Metropolis algorithm. We study the chiral transition in the chiral limit
and focus on the dependence of the second-order chiral transition temperature
$aT_c$ for different values of the lattice gauge coupling $\beta$. We compare
different orders of truncations of the strong coupling expansion:
$Ord(\beta^0)$, $Ord(\beta^1)$, and $Ord(\beta^2)$. We comment on the prospects
of extending to $SU(3)$ at finite density.
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