(A) Binary 128×128 lattices showing the configuration of spins after 2,000 timesteps at low temperature,

(left); critical temperature,

(middle); and high temperature,

(right). At hot temperature the spins are randomly configured, at low temperature they are close to an entirely ordered state, and at critical temperature they have a fractal configuration. (B) Probability distribution of phase lock interval (PLI) between pairs of processes at critical (black line) and at hot temperature (red line) plotted on a log-log scale. The black dashed line represents a power law with slope

. (C) Probability distribution of lability of global synchronization (

) at critical temperature (black line) and at hot temperature (red dotted line); the black dashed line represents a power law with slope

. For the cold Ising model the equilibrium state of the system is a monolithic lattice with either all spins up or down, resulting in an entirely static system for which the PLI distribution is a Dirac Delta peak at the duration of the time series. The key point is that the probability distributions of both duration of pairwise synchronization, indexed by the phase lock interval, and lability of global synchronization, show power law behaviour for the 2D Ising model specifically at critical temperature.

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