Ising model can also account for the nucleation dynamics of the Mott transition.

The phase transformation dynamics is conventionally formulated in terms of the appropriate order parameters that characterize the phase transition [@binder87; @onuki02]. However, since the MIT is a transition between different transport behaviors and is not characterized by broken symmetries, there is no clear choice of the order parameter. For Mott transitions, however, making use of the analogy with the liquid-gas transition, one can introduce an order parameter based on, e.g. the density of doublons, or doubly occupied sites [@lee17]. Since the Gutzwiller method can be viewed as a mean-field theory of the Mott transition within the Kotliar-Ruckenstein slave-boson framework [@kotliar86], it offers a systematic construction of the relevant order parameters. Specifically, they correspond to the coherent state $\Phi$ of the slave bosons [@lanata12; @lanata15]. For example, $\Phi$ in the single-band Hubbard model is represented by the amplitudes $\Phi = (e, p_{ \uparrow}, p_{ \downarrow}, d)$, whose square give the probability of the empty, singly occupied (up and down spin), and doubly occupied states, respectively [@kotliar86]. It thus encodes information about the local electron density $n_\alpha = |p_\alpha|^2$ as well as the double occupancy $D = |d|^2$. This 