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The 2D Ising model, criticality and AIT

View ORCID ProfileG. Ruffini, View ORCID ProfileG. Deco
doi: https://doi.org/10.1101/2021.10.21.465265
G. Ruffini
aNeuroelectrics Corporation, Cambridge, 02139 MA, USA
bNeuroelectrics Barcelona, Av. Tibidabo 47bis, 08035, Barcelona, Spain
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  • For correspondence: giulio.ruffini@neuroelectrics.com
G. Deco
cInstitució Catalana de Recerca i Estudis Avançats (ICREA), Universitat Pompeu Fabra, Computational Neuroscience, Plaça de la Mercè, 10–12, 08002 Barcelona, Spain
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Abstract

In this short note we study the 2D Ising model, a universal computational model which reflects phase transitions and critical phenomena, as a framework for establishing links between systems that exhibit criticality with the notions of complexity. This is motivated in the context of neuroscience applications stemming from algorithmic information theory (AIT). Starting with the original 2D Ising model, we show that — together with correlation length of the spin lattice, susceptibility to a uniform external field — the correlation time of the magnetization time series, the compression ratio of the spin lattice, the complexity of the magnetization time series — as derived from Lempel-Ziv-Welch compression—, and the rate of information transmission in the lattice, all reflect the effects of the phase transition, which results in spacetime pockets of uniform magnetization at all scales. We also show that in the Ising model the insertion of sparse long-range couplings has a direct effect on the critical temperature and other parameters. The addition of positive links extends the ordered regime to higher critical temperatures, while negative links have a stronger, disordering influence at the global scale. We discuss some implications for the study of long-range (e.g., ephaptic) interactions in the human brain and the effects of weak perturbations in neural dynamics.

Competing Interest Statement

The authors have declared no competing interest.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted October 22, 2021.
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The 2D Ising model, criticality and AIT
G. Ruffini, G. Deco
bioRxiv 2021.10.21.465265; doi: https://doi.org/10.1101/2021.10.21.465265
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The 2D Ising model, criticality and AIT
G. Ruffini, G. Deco
bioRxiv 2021.10.21.465265; doi: https://doi.org/10.1101/2021.10.21.465265

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