is mainly determined by the interface energy which can be expressed as $\varepsilon(A) = \sigma A$, where $\sigma$ is the surface tension and $A \sim s^{(d-1)/d}$ is the surface area of the nuclei with size $s$. In two dimensions their distribution, given by the Boltzmann probability, is then $$\begin{aligned}
    \label{eq:ns_exp}
    n(s, t) \sim \exp(- \beta \sigma_{\rm eff} \sqrt{s}),  \end{aligned}$$ where $\sigma_{\rm eff}$ is an effective surface tension. As shown in Fig. \[fig:histogram\], the expression in Eq. (\[eq:ns\_exp\]) indeed fits the numerical distributions very well for small $s$, particularly at the initial stage of the phase transformation. The effective surface tension obtained from the fitting is $\sigma_{\rm eff} \approx 0.1$.

![(Color online) \[fig:histogram\] The probability distribution function $n(s)$ of the size of Mott clusters at different stages, characterized by the volume fraction of the Mott clusters, of the phase transformation. The curves are shifted vertically for clarity. The corresponding curve of volume fraction $\phi_M$ versus time is shown in Fig. \[fig:trace\](b). Each curve is obtained by average over a small time interval $[t-\Delta t, t+\Delta t]$ with $\Delta t = 2.5$, and over 15 independent simulations. The solid lines are the fit using Eq. (\[eq:ns\_exp\]). The dashed line corresponds to power 