22-77 Joe Neeman, Charles Radin, Lorenzo Sadun

Existence of a symmetric bipodal phase in the edge-triangle model (588K, pdflatex) Nov 19, 22

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Abstract. In the edge-triangle model with edge density close to 1/2 and triangle density below 1/8 we prove that the unique entropy-maximizing graphon is symmetric bipodal. We also prove that, for any edge density $e$ less than $e_0 = (3-\sqrt{3})/6 pprox 0.2113$ and triangle density slightly less than $e^3$, the entropy-maximizing graphon is not symmetric bipodal.

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