  Gravitational waves can be used to test general relativity (GR) in the highly
dynamical strong-field regime. Scalar-tensor theories of gravity are natural
alternatives to GR that can manifest nonperturbative phenomena in neutron stars
(NSs). One such phenomenon, known as dynamical scalarization, occurs in
coalescing binary NS systems. Ground-based gravitational-wave detectors may be
sensitive to this effect, and thus could potentially further constrain
scalar-tensor theories. This type of analysis requires waveform models of
dynamically scalarizing systems; in this work we devise an analytic model of
dynamical scalarization using an effective action approach. For the first time,
we compute the Newtonian-order Hamiltonian describing the dynamics of a
dynamically scalarizing binary in a self-consistent manner. Despite only
working to leading order, the model accurately predicts the frequency at which
dynamical scalarization occurs. In conjunction with Landau theory, our model
allows one to definitively establish dynamical scalarization as a second-order
phase transition. We also connect dynamical scalarization to the related
phenomena of spontaneous scalarization and induced scalarization; these
phenomena are naturally encompassed into our effective action approach.
