Localization transition in the Mermin model

We study the dynamical properties of the Mermin model, a simple quantum dissipative model with a monochromatic environment, using analytical and numerical methods. Our numerical results show that the model exhibits a second order phase transition to a localized state before which the system is effectively decoupled from the environment. In contrast to the spin-boson model, the Mermin model exhibits an ``orthogonality catastrophe,'' defining the critical point, before dissipation has destroyed all coherent behavior. An analytic approach based on the Liouvillian technique, although successful in describing the phase diagram of spin-boson and related models, fails to capture this essential feature of the Mermin model.