Squeezing order out of disorder*

Computable Information Density (CID), the ratio of the length of a losslessly compressed data file to that of the uncompressed file, is a measure of order and correlation in both equilibrium and nonequilibrium systems. I will show that correlation lengths can be obtained by decimation, thinning a configuration by sampling data at increasing intervals and recalculating the CID. When the sampling interval increases above the system’s correlation length, correlations vanish and the data becomes incompressible. The correlation length critical exponents are thus accessible with no a-priori knowledge of an order parameter or even the nature of the ordering. The critical scalings for the length scales obtained by CID agree well with those from the decay of two-point correlation functions g₂(r) when they exist. But CID also reveals a correlation length with the right scaling when g₂(r) = 0, as we demonstrate by “cloaking” the data with a Rudin-Shapiro sequence. Finally, I will show how CID revealed previously unknown ordering phenomena, such as a cascade of phase transitions in the BML traffic model, and a "checkerboard" dynamical instability in the parallel update Manna sandpile model.