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. Here we 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 is larger than the system's correlation length, the data becomes incompressible. The correlation length and its critical exponents are thus accessible with no a priori knowledge of an order parameter or even the nature of the ordering. The correlation length measured in this way agrees well with that computed from the decay of two-point correlation functions g2(r) when they exist. But the CID reveals the correlation length and its scaling even when g2(r) has no structure, as we demonstrate by "cloaking"the data with a Rudin-Shapiro sequence.
Bibliographical noteFunding Information:
We particularly thank Yariv Kafri for crucial discussions at many stages of this project. This work was primarily supported by the National Science Foundation Physics of Living Systems Grant No. 1504867. D. L. thanks the U.S.-Israel Binational Science Foundation (Grant No. 2014713), the Israel Science Foundation (Grant No. 1866/16). P. M. C. was supported partially by the Materials Research Science and Engineering Center (MRSEC) Program of the National Science Foundation under Award No. DMR-1420073.
PubMed: MeSH publication types
- Journal Article