论文标题
相关长度在可计算信息的语言中
Correlation lengths in the language of computable information
论文作者
论文摘要
可计算的信息密度（CID）是无损压缩数据文件与未压缩文件的长度的比率，是平衡和非平衡系统的顺序和相关性的度量。在这里，我们表明可以通过拆卸来获得相关长度 - 通过增加间隔并重新计算CID来使配置稀疏配置。当采样间隔大于系统的相关长度时，数据变得不可压缩。因此，相关长度及其关键指数无法访问，而没有对订单参数甚至订购性质的A-Priori知识。以这种方式测量的相关长度与从两点相关函数的衰减$ g_ {2}（r）$计算得很好的一致。但是，即使$ g_ {2}（r）$没有结构，CID即使我们通过用Rudin-Shapiro序列“掩盖”数据来揭示相关长度及其缩放。
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 $g_{2}(r)$ when they exist. But the CID reveals the correlation length and its scaling even when $g_{2}(r)$ has no structure, as we demonstrate by "cloaking" the data with a Rudin-Shapiro sequence.
