Macroscopic loops exist in the random loop model on sparse random graphs above an explicit edge density threshold depending on loop weight θ and cross parameter u.
MacroscopiccyclesfortheinterchangeandquantumHeisenberg models on random regular graphs
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Macroscopic loops in the random loop model on sparse random graphs
Macroscopic loops exist in the random loop model on sparse random graphs above an explicit edge density threshold depending on loop weight θ and cross parameter u.