In a mean-field analysis, the simplicial Ising model on hypergraphs shows continuous transitions for hyperedge sizes up to 4 and discontinuous transitions for larger sizes, with richer double and mixed-order behavior when pairwise edges coexist.
Bianconi, Higher-order networks (Cambridge Univer- sity Press, 2021)
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Phase Transitions in the Simplicial Ising Model on Hypergraphs
In a mean-field analysis, the simplicial Ising model on hypergraphs shows continuous transitions for hyperedge sizes up to 4 and discontinuous transitions for larger sizes, with richer double and mixed-order behavior when pairwise edges coexist.