Figure 1

The $\Gamma -\delta$ phase diagram shows three phases: a fluid at high temperatures, a crystal, and a inhomogeneous solid ($I$ phase). The boundary between the crystal and the $I$ phase lies at $0.18<{\delta }_c<0.21$. The vertical line in the fluid phase is the kinetic glass transition. (Inset) Integrated relaxation time [16], $\tau$, for $e$ (full) and $\mathcal{F}$ (open), both for standard (squares) and local swap (circles) MC, for $N=256$. The kinetic glass transition arises when $\tau \sim {10}^6$ standard MC steps.Reuse & Permissions

Figure 2

Equilibrium quantities for $\delta =0.24$ (top left) specific heat vs $\Gamma$, from two simulations, one at the size dependent critical point (full symbols denote the actual simulations, full lines coming from histogram reweighting), the other at a higher $\Gamma$ (open symbols and dashed lines). The maximum of the specific heat scales with $N$. (Top right) $⟨\mathcal{F}⟩/N$ vs $\Gamma$ for the same simulations of top-left panel. (Bottom left) Normalized histogram, $f$, of the energy of the inherent structures, for $N=256$ (empty) and $N=500$ (filled), at the $\Gamma$ value where the peaks of the instantaneous energy have equal height [20]. Inherent structures were found every ${10}^5$ MC steps. (Bottom right) As bottom left, for $\mathcal{F}$. In the fluid phase $\mathcal{F}$ is $\mathcal{O}(1)$ [in the solid, $\mathcal{F}$ is $\mathcal{O}(N)$]. We also show (dashed line) $e_{\mathrm{is}}$ and $\mathcal{F}$ histograms for $N=864$, where only two back and forth tunneling events between the liquid and solid phase were observed. Yet, data nicely agree with the predicted $N$ scaling.Reuse & Permissions

Figure 3

Scatter plot of $\mathcal{F}$ vs $e_{\mathrm{is}}$ below (bottom) and above (top) the $I$-phase-crystal transition line at the liquid-solid phase coexistence, for $N=256$ (left) and $N=500$ (right). The number of points is $\sim 45000$ ($N=256$) or $\sim 15000$ ($N=500$). The darker the shade of gray, the higher the density of points.Reuse & Permissions

Figure 4

(Top left) A $\delta =0.3$ solid configuration of 500 particles, at phase coexistence, as projected into the $XY$ plane (circles are centered at particles positions, their diameter being proportional to particle sizes). Larger particles form the crystalline central band (the Bragg peaks’s analysis suggests a FCC ordering). Normalized histograms of $\mathcal{B}$ for $\delta =0.24$, 0.3, 0.45 with 256 (empty) and 500 (filled) particles.Reuse & Permissions