Fig. 10
From: Order–disorder phase transitions of phosphorene and their application to adiabatic quantum computing
Autocorrelation function C(t) for different phases over Monte Carlo time. This figure presents the evolution of the spin autocorrelation function C(t) for four phases: (a) Checkerboard and Checker-Stripy phases (linear scale), (b) Checkerboard and Checker-Stripy phases (log scale), (c) Glassy and Paramagnetic phases (linear scale), and (d) Glassy and Paramagnetic phases (log scale). In the checkerboard phase (a), the autocorrelation function remains near 1, indicating a stable, ordered state with minimal fluctuations over Monte Carlo time. Similarly, the checker-stripy phase (a) shows fluctuations, but with a slow decay around well-defined values, suggesting partial stability, though the system transitions between several configurations. The log scale plot of the checkerboard and checker-stripy phases (b) reveals the slow decay in C(t) for the checker-stripy phase, where the system fluctuates between distinct values over time, reflecting the multiple stable configurations of this phase. The log scale makes it clearer that the checker-stripy phase gradually shifts between stable configurations but does not settle into a unique, globally stable state, reinforcing its quasi-ordered nature. In the glassy phase (c), the autocorrelation function remains constant over time, indicating that the system is trapped in a local minimum, consistent with the lack of available energy to escape this configuration at low temperatures. The paramagnetic phase (c) shows rapid fluctuations around zero, confirming its disordered nature.
