  Quantum Zeno and anti-Zeno effects on pure dephasing are studied using
exactly solvable microscopic models. The crossover between these two opposite
effects is investigated. The case of a single two-level system undergoing
dephasing is already different from the previously studied population decay
problem, even without taking into account any back action from the environment.
For many two-level systems interacting with a common environment, multiple
transitions between Zeno and anti-Zeno regimes are predicted. Finally, if the
system-environment coupling strength is not weak, we show that the nontrivial
evolution of the environment between measurements can considerably alter the
quantum Zeno and anti-Zeno effects.
