Collapse of Transient Nucleation Fluxes in a Cold Ising Ferromagnet

We report the time-dependent nucleation fluxes and associated nucleation rates in a metastable Ising ferromagnet on square lattice with Metropolis (Glauber-type) dynamics. It is discovered that, with lowering of the temperature, fluxes collapse into several representative transient curves corresponding to magic cluster sizes. Those can be associated with physical droplets, i.e., long-lived configurations which provide a link with the classical Becker-Döring picture.

Figure 1

Collapse of transient fluxes $J_n(t)/J_{\mathrm{st}}$ with lowering of the temperature. Left column: $h=0.22$, $0\le n\le 20$. Right column: $h=0.15$, $1\le n\le 25$. At higher $T$, the structure of fluxes is similar to the one in the Becker-Döring model, including the overshoot at subcritical $n$ [4]. At low $T$, fluxes group into a few representative curves. For $T=0.2$, $h=0.22$, the groups are (counterclockwise, from top): $n=(0–3)$, $(4,5)$ (the two descending curves) and $n=(6,7)$, 8, (9–11), (12–14), 15, (16–19), 20. For $h=0.15$, the second group is $n=(4–11)$ (descending), and added groups on the right (due to larger $n_D$) are $n=(20–23)$, 24, 25. At intermediate $T=0.4$, similar grouping is observed, although collapse is incomplete; the $(4,5)$ fluxes for $h=0.22$ and the $(9,10)$ and the 11 fluxes for $h=0.15$ are shown as bell-shaped, rather than descending, curves due to a smaller overshoot at higher $T$.

Figure 2

Reduced nucleation rates [fluxes $J_n(t)/J_{\mathrm{st}}$ at the largest $n$ in Fig. 1] vs the scaling parameter $x=[t-t_0]/t_{\mathrm{rel}}+0.5772\dots$ at different temperatures and fields. The parameters $t_0$ and $t_{\mathrm{rel}}$ can be calculated from exact expressions (see text) and are indicated in the legend. Scaled data closely follow the double-exponential shape (solid line) expected from the Becker-Döring model [13].