Correlation Lengths in the Language of Computable Information.
Stefano Martiniani1,2, Yuval Lemberg3, Paul M Chaikin2
1Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA.
Physical Review Letters
|November 6, 2020
Summary
Computable information density (CID) measures system order. Decimation and CID recalculation reveal correlation lengths, even in complex systems lacking traditional order parameters.
Area of Science:
- Complex systems analysis
- Information theory
- Statistical physics
Background:
- Computable information density (CID) quantifies data order and correlation.
- Existing methods for correlation length measurement often require prior knowledge of order parameters.
Purpose of the Study:
- To introduce a novel method for determining correlation lengths using CID.
- To demonstrate the method's applicability in systems lacking apparent order parameters.
Main Methods:
- Data decimation: progressively thinning data by increasing sampling intervals.
- Recalculating CID at each decimation step to identify the point of incompressibility.
- Comparing CID-derived correlation lengths with traditional two-point correlation functions.
Main Results:
- Decimation reveals system correlation lengths when CID becomes incompressible.
- This method successfully determines correlation lengths and critical exponents without a priori knowledge.
- The technique is effective even when standard two-point correlation functions lack structure, as shown with Rudin-Shapiro sequences.
Conclusions:
- Decimation-based CID analysis offers a universal approach to measure correlation lengths.
- This method provides insights into system order and critical phenomena across diverse systems.
- It overcomes limitations of traditional methods, enabling analysis of complex and unconventional data.
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