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We study the effects of random pinning on the Fredrickson-Andersen model onthe Bethe lattice. We find that the nonergodic transition temperature rises asthe fraction of the pinned spins increases and the transition line terminatesat a critical point. The freezing behavior of the spins is analogous to that ofa randomly pinned p-spin mean-field spin glass model which has been recentlyreported. The diverging behavior of correlation lengths in the vicinity of theterminal critical point is found to be identical to the prediction of theinhomogeneous mode-coupling theory at the A3 singularity point for the glasstransition.

Fredrickson-Andersen model on Bethe lattice with random pinning