{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T21:49:05Z","timestamp":1777412945737,"version":"3.51.4"},"reference-count":56,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T00:00:00Z","timestamp":1584316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN\/05578-2014"],"award-info":[{"award-number":["RGPIN\/05578-2014"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Integrated Information Theory (IIT) posits that integrated information (   \u03a6   ) represents the quantity of a conscious experience. Here, the generalized Ising model was used to calculate    \u03a6    as a function of temperature in toy models of fully connected neural networks. A Monte\u2013Carlo simulation was run on 159 normalized, random, positively weighted networks analogous to small five-node excitatory neural network motifs. Integrated information generated by this sample of small Ising models was measured across model parameter spaces. It was observed that integrated information, as an order parameter, underwent a phase transition at the critical point in the model. This critical point was demarcated by the peak of the generalized susceptibility (or variance in configuration due to temperature) of integrated information. At this critical point, integrated information was maximally receptive and responsive to perturbations of its own states. The results of this study provide evidence that    \u03a6    can capture integrated information in an empirical dataset, and display critical behavior acting as an order parameter from the generalized Ising model.<\/jats:p>","DOI":"10.3390\/e22030339","type":"journal-article","created":{"date-parts":[[2020,3,17]],"date-time":"2020-03-17T09:27:41Z","timestamp":1584437261000},"page":"339","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["The Emergence of Integrated Information, Complexity, and \u2018Consciousness\u2019 at Criticality"],"prefix":"10.3390","volume":"22","author":[{"given":"Nicholas J.M.","family":"Popiel","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, Western University, 151 Richmond St, London, ON N6A 3K7, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3701-1734","authenticated-orcid":false,"given":"Sina","family":"Khajehabdollahi","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Western University, 151 Richmond St, London, ON N6A 3K7, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7595-5237","authenticated-orcid":false,"given":"Pubuditha M.","family":"Abeyasinghe","sequence":"additional","affiliation":[{"name":"Faculty of Medicine Nursing and Health Sciences, Monash University, Wellington Rd, Clayton VIC 3800, Australia"}]},{"given":"Francesco","family":"Riganello","sequence":"additional","affiliation":[{"name":"Research in Advanced Neurorehabilitation (RAN), S. Anna Institute, Via Siris 11, 88900 Crotone, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0541-9233","authenticated-orcid":false,"given":"Emily S.","family":"Nichols","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Western University, 151 Richmond St, London, ON N6A 3K7, Canada"},{"name":"Brain and Mind Institute, Western University, 151 Richmond St, London, ON N6A 3K7, Canada"}]},{"given":"Adrian M.","family":"Owen","sequence":"additional","affiliation":[{"name":"Brain and Mind Institute, Western University, 151 Richmond St, London, ON N6A 3K7, Canada"},{"name":"Department of Psychology and Department of Physiology and Pharmacology, 151 Richmond St, London, ON N6A 3K7, Canada"}]},{"given":"Andrea","family":"Soddu","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Western University, 151 Richmond St, London, ON N6A 3K7, Canada"},{"name":"Brain and Mind Institute, Western University, 151 Richmond St, London, ON N6A 3K7, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1038\/nphys2190","article-title":"Between order and chaos","volume":"8","author":"Crutchfield","year":"2012","journal-title":"Nat. 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