  We benchmark recently proposed tensor network based finite-size scaling
analysis in Phys. Rev. B 107, 205123 (2023) against two-dimensional classical
3-state clock model. Due to the higher complexity of the model, more
complicated crossover behavior is observed. We advocate that the crossover
behavior can be understood from the perspective of finite bond dimension
inducing relevant perturbation. This leads to a general strategy to best
estimate the critical properties for a given set of control parameters.For the
critical temperature $T_c$, the error at the order of $10^{-6}$ can be reached
with bond dimension $D=70$. On the other hand, with bond dimension $D=60$, the
error of the critical exponents $\nu, \beta, \alpha$ is at the order of
$10^{-3}$.Increasing the bond dimension to $D=90$, the error of $\nu$ and
$\beta$ can be reduced to the order of $10^{-4}$, but for some calculations
numerical instability starts to emerge. In all cases our results indicate that
the errors can be systematically reduced by increasing the bond dimension and
the stacking number.
