be directly combined with large-scale simulations. One exception is the Gutzwiller approach [@gutzwiller63; @gutzwiller64; @gutzwiller65], which allows for computational efficiency similar to the Hartree-Fock methods or the density functional theory (DFT). Importantly, the Gutzwiller method captures essential correlation effects such as the bandwidth renormalization and electron localization [@brinkman70], and offers perhaps the only feasible way for large-scale real-space simulations of MIT.

The mesoscale electronic inhomogeneities associated with the MIT are reminiscent of the complex patterns observed in numerous first-order phase transitions of, e.g. binary alloys, polymer mixtures, and many other physical systems [@langer80; @gunton83; @puri09]. The study of the first-order transition kinetics has a long history [@binder87; @onuki02]. Microscopically, the kinetic Ising model with, e.g. Glauber-type dynamics, has been extensively used to simulate the phase transformation dynamics [@marro79; @phani80; @sadiq83; @stauffer82; @shneidman99; @shneidman99b; @wonczak00; @soisson00; @brendel05; @ryu10; @binder16]. The Ising, or the liquid-gas, transition is also often invoked to model the Mott MIT by, e.g. associating the gas and liquid phases with the metallic phase and Mott insulator, respectively [@limelette03; @bartosch10; @itou17; @liu16; @bar18; @papanikolaou08]. Several works have indicated that Mott transitions likely belong to the Ising universality class. One objective of this work is to investigate whether the kinetic 