Figure 1

Monte Carlo results of the elastic energy with $N_p$ polarons on a $55\times 55$ lattice as a function of temperature for $N_p=2,5,16,30,50$.Reuse & Permissions

Figure 2

The strain $e_1$ for 50 polarons on a $55\times 55$ lattice and for different temperatures. (a) Polaron stripe at zero temperature. (b) Low-temperature transition regime $T=0.38$. The long stripe becomes unstable and a small number of polarons escape, moving alone or forming smaller stripes. (c) Intermediate-temperature transition regime with $T=0.42$. The long stripe is almost completely destroyed. Individual polarons move on the lattice and form smaller stripes with a finite lifetime. (d) High-temperature regime with $T=0.6$. All polarons move independently: Small stripes are formed but their lifetime is very short.Reuse & Permissions

Figure 3

Hysteresis loop when a system of 55 polarons is cooled, starting with a thermalized polaron gas at high temperatures. The upper line is the energy when cooled from the polaron gas, while the lower line corresponds to the average energy upon heating the system starting with a stripe at $T=0$. When the system is cooled, it freezes into a higher-energy glassy state with many smaller stripes. The dashed line is the average energy obtained by reheating the system starting from the frozen, many stripes glassy state obtained upon cooling.Reuse & Permissions

Figure 4

The strain field $e_1$ obtained from cooling an initially thermalized polaron gas at high $T$. (a) The frozen glassy state with many stripes ($T=0$). (b) Intermediate temperature $T=0.34$ where the glassy state is almost formed. (c) The initial high-temperature polaron gas for $T=0.6$.Reuse & Permissions

Figure 5

Pair distribution function density plot as a function of temperature for $N_p=30$ on a $55\times 55$ lattice. A regular arrangement of delta-function peaks with zero background fluctuations is seen for small temperatures, but as the temperature increases the long-range correlation becomes weaker and the corresponding peaks are replaced by a background fluctuation. At even higher temperatures, even the short-range correlations disappear and the pair distribution becomes almost uniform.Reuse & Permissions