Monte Carlo Study of the Quenched Eguchi-Kawai Model

The quenched Eguchi-Kawai model is studied by using the Monte Carlo technique. The data indicate that in the large-$N$ limit the quenched Eguchi-Kawai model is identical to the Wilson theory throughout the whole range of coupling constants. The first-order phase transition is observed at $\frac{\beta }{N}=0.29\mathrm{}\pm 0.02$ for the gauge group U(20).