The 2D Ising model, criticality and AIT

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.

AIT Foundations of Structured Experience

“…This agrees with the notion of apparent complexity from simplicity and the prediction [Ruffini, 2017;Ruffini et al, 2018] that healthy agents running models generate apparently complex data (entropic but hierarchically organized), as anticipated by Wolfram [2002]. The relationship between critical features of simple systems such as the Ising model and algorithmic complexity has been studied in Ruffini & Deco [2021]. In Ruffini et al [2022a], criticality aspects induced by psychedelics using the Ising model were analyzed, and it was shown that the Ising temperature is a relevant biomarker for the study of the effects of psychedelics: the resting brain, already found to be above the model's critical temperature, is further shifted into disorder under the effects of LSD.…”

“…Near criticality, complex systems generate structured data with power-laws and high entropy (apparent complexity). Notably, these systems will display enhanced sensitivity to weak perturbations, maximal information flow and long spatiotemporal scales [Ruffini & Deco, 2021], and the dynamics of the system collapse to a lower dimensional (center) manifold [Jirsa & Sheheitli, 2022]. Experimental data suggests that our brains operate close to such critical boundaries [Bak et al, 1988;Chialvo, 2004;Cocchi et al, & Friston, 2019;Ruffini et al, 2022a].…”

A multi-layer mean-field model for the cerebellar cortex: design, validation, and prediction

“…Among these it is worth mentioning ataxias (Pedroso et al, 2019; Rosenthal, 2022), paroxysmal dyskinesia (Mendonça and Alves da Silva, 2021; Ekmen et al, 2022), dystonia (Mahajan et al, 2021; Morigaki et al, 2021), autistic spectrum disorders (Bruchhage et al, 2018; Kelly et al, 2020) as well as other pathologies like and multiple sclerosis (Tornes et al, 2014; Schreck et al, 2018), dementia (Monteverdi et al, 2022) and Parkinson disease (Wu and Hallett, 2013; Shen et al, 2020), in which a cerebellum involvement has been reported. The cerebellar MF could be applied to whole-brain simulators using TVB and DCM, as much as it has been done before for the isocortical MF in TVB (Pinotsis et al, 2012; Goldman et al, 2019; Sadeghi et al, 2020; Ruffini and Deco, 2021). Considering the specificity of signal processing in different brain regions, this approach represents a definite step ahead compared to the classical one adopting generic neural masses for all brain regions.…”

LSD-induced increase of Ising temperature and algorithmic complexity of brain dynamics

“…Additionally, the system’s temperature regulates its phase transitions, and hence its value establishes how far it is from criticality. In addition, given the potential relationship between signal diversity, algorithmic complexity, criticality, and brain state, we explore complexity metrics characterizing the two conditions in the data with the hypothesis that complexity correlates with system temperature [65, 64, 68].…”

“…Moreover, the system’s temperature situates the state in relation to the critical boundaries defining phase transitions. Finally, given the intuitive relationship between signal diversity, algorithmic complexity, and criticality, we explore complexity metrics characterizing the two conditions in the data with the hypothesis that complexity correlates with system temperature and hence experimental condition [2, 3, 51].…”