law $s^{-\tau'}$ with $\tau' = 1.42$. The estimated error of the exponent is $\pm 0.06$. ](histogram.pdf){width="0.95\columnwidth"}

Significant deviation from Eq. (\[eq:ns\_exp\]) starts to occur at cluster size $s_c \approx 100$, which provides an estimate for the so-called critical size. The concept of critical nuclei was first discussed in the classical droplet model. In this picture, the decay of a meta-stable state is initiated by a collection of independent fluctuating droplets. Their quasi-equilibrium distribution is again given by the Boltzmann probability $n_0(s) \propto \exp[- \beta \varepsilon(s)]$, where $\varepsilon(s)$ is the minimum work required to form a cluster of size $s$. In general $d$ dimensions, this minimum work is $$\begin{aligned}
    \varepsilon(s) = \sigma s^{(d-1)/d} + \Delta f\, s.\end{aligned}$$ The first term represents the interface energy as discussed above, while the second term denotes the volume energy of the droplets with $\Delta f$ being the free-energy difference between the two competing phases. For $\Delta f > 0$, the droplets correspond to thermodynamically unfavorable phase, and $n_0(s)$ describes the fluctuations of these small domains. On the other hand, for $\Delta f < 0$, as in a quench into meta-stable states, $\varepsilon(s)$ describes the competition between the surface tension and the volume energy gain. In 