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Phase transitions on complex hypergraphs
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- Statistical physics solves models on networks by pretending they are trees, and real networks are not: the neighbours of a node are neighbours of one another, because interactions are group-level. Proteins act in complexes, a paper has six authors, a reaction consumes three species. The answer here is to stop treating a dense knot as many links and treat it as one thing. A complex hypergraph, or chygraph, is a set of complexes whose vertices are themselves complexes. Graphs, hypergraphs, multiplex networks and simplicial complexes are all chygraphs differing only in their layer data, and a clustered graph becomes treelike over complexes once its motifs are promoted. One cavity recursion then serves every model. Percolation reduces to one self-consistency map whose threshold is fixed by four moment matrices of layer dimension; replace the message with a measure and the Ising model follows, with an integer the hitting set problem, with three states vertex cover, with a distribution over q colours colouring, with a warning satisfiability. Only the message changes; the interior of a complex is summed exactly. Several results are counterintuitive: clustering lowers the Ising critical temperature; the standard zero-temperature limit is wrong on hypergraphs. Part IV measures where it fails and what repairs it.
| Publisher | Independently published |
| Publication date | September 5, 2026 |
| Language | English |
| Print length | 539 pages |
| ISBN-13 | 979-8172042287 |
| Item Weight | 1.49 pounds (680 grams) |
| Dimensions | 5 x 1.22 x 8 inches (12.7 x 3.1 x 20.3 cm) |
Product Description
Phase transitions on complex hypergraphs
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