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We benchmark recently proposed tensor network based finite-size scalinganalysis in Phys. Rev. B 107, 205123 (2023) against two-dimensional classical3-state clock model. Due to the higher complexity of the model, morecomplicated crossover behavior is observed. We advocate that the crossoverbehavior can be understood from the perspective of finite bond dimensioninducing relevant perturbation. This leads to a general strategy to bestestimate the critical properties for a given set of control parameters.For thecritical temperature $T_c$, the error at the order of $10^{-6}$ can be reachedwith bond dimension $D=70$. On the other hand, with bond dimension $D=60$, theerror 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 calculationsnumerical instability starts to emerge. In all cases our results indicate thatthe errors can be systematically reduced by increasing the bond dimension andthe stacking number.

Tensor Network Finite-Size Scaling for Two-Dimensional 3-state Clock Model