Analysis of the phase transition in the two-dimensional Ising ferromagnet using a Lempel-Ziv string-parsing scheme and black-box data-compression utilities

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
O Melchert, A K Hartmann

Abstract

In this work we consider information-theoretic observables to analyze short symbolic sequences, comprising time series that represent the orientation of a single spin in a two-dimensional (2D) Ising ferromagnet on a square lattice of size L(2)=128(2) for different system temperatures T. The latter were chosen from an interval enclosing the critical point T(c) of the model. At small temperatures the sequences are thus very regular; at high temperatures they are maximally random. In the vicinity of the critical point, nontrivial, long-range correlations appear. Here we implement estimators for the entropy rate, excess entropy (i.e., "complexity"), and multi-information. First, we implement a Lempel-Ziv string-parsing scheme, providing seemingly elaborate entropy rate and multi-information estimates and an approximate estimator for the excess entropy. Furthermore, we apply easy-to-use black-box data-compression utilities, providing approximate estimators only. For comparison and to yield results for benchmarking purposes, we implement the information-theoretic observables also based on the well-established M-block Shannon entropy, which is more tedious to apply compared to the first two "algorithmic" entropy estimation procedures....Continue Reading

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Citations

Mar 3, 2018·Chaos·E Estevez-RamsB Aragón-Fernández
May 9, 2019·PloS One·Ernesto Estevez-RamsDaniel Estevez-Moya
Nov 9, 2019·Physical Review Letters·Ram AvineryRoy Beck
Sep 19, 2020·Physical Review. E·Gil Ariel, Haim Diamant
Jun 5, 2018·Entropy·António M Lopes, J A Tenreiro Machado
Nov 20, 2020·Proceedings of the National Academy of Sciences of the United States of America·Andrey A BagrovVladimir V Mazurenko

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