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Emergence in graphs with near-extreme constraints

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abstract

We consider entropy-optimal graphons associated with extreme and near-extreme constraints on the densities of edges and triangles. We prove that the optimizers for near-extreme constraints are unique and multipodal and are perturbations of the previously known unique optimzers for extreme constraints. This proves the existence of infinitely many phases. We determine the podal structures in these phases and prove the existence of phase transitions between them.

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representative citing papers

Superfluid helium

cond-mat.stat-mech · 2026-08-05 · conditional · novelty 4.0

The edge/triangle graph model gives a solvable toy analog in which a symmetry-based order parameter distinguishes the helium I and helium II phases.

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  • Superfluid helium cond-mat.stat-mech · 2026-08-05 · conditional · none · ref 49 · internal anchor

    The edge/triangle graph model gives a solvable toy analog in which a symmetry-based order parameter distinguishes the helium I and helium II phases.