2023/04/27 by Otávio Cistolo Citton, Citton, Otavio, Nestor Caticha +1
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Condensed matter physics #Data mining #Discrete mathematics #FOS: Physical sciences #Homogeneous #Ising model #Mathematics #Measure (data warehouse) #Modular design #Neural Networks and Applications #Partition (number theory) #Physics #Quantum many-body systems #Spins #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #Statistical physics
paper · pdf · doi:10.48550/arxiv.2304.14316
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the possible applications that a better understanding of consciousness might bring, we follow Tononi's idea and calculate analytically a complexity index for two systems of Ising spins with parallel update dynamics, the homogeneous and a modular infinite range models. Using the information geometry formulation of integrated information theory, we calculate the geometric integrated information index, ϕG(Π) for a fixed partition Π with K components and Φ=maxΠϕG(Π) for K=2 or 3. For systems in the deep ferromagnetic phase, the optimal partition undergoes a transition such that the smallest (largest) component is above (resp. below) its critical temperature. The effects of partitioning are taken into account by introducing site dilution.