model with the standard twist. Our work in this article is along this line and we mainly concentrate on investigating locations of the symmetry breaking from the weak coupling side in $(\beta, N)$ plane. By the Monte-Carlo simulation we clarify the linear behavior of critical lattice coupling $$\beta_c^L\sim L^2,  
\label{EQ:scaling_of_beta_c^L}$$ where $\beta_c^L$ represents critical lattice coupling from the weak coupling side and $L$ is the lattice size we have considered. This result means that [*the continuum limit of the planar gauge theory cannot be described by the TEK model*]{} from the argument of the scaling behavior around the weak coupling limit. This discussion can be also applied to the NCYM case.

This article is organized as follows. In the next section we review the TEK model briefly and fix our setup. In section \[SEC:breaking\] we show the numerical results for the $\mathbb{Z}_N^D$ symmetry breaking of the TEK model and find the scaling behavior (\[EQ:scaling\_of\_beta\_c\^L\]). In section \[SEC:discussions\] we give the validation for the numerical result, and also discuss whether the TEK model has a continuum limit or not.

Twisted Eguchi-Kawai model
==========================

Action and Wilson loop
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In this study, we treat the $D=4$ case. The TEK model [@GonzalezArroyo:1982ub] is 