Non-uniqueness of phase transitions for graphical representations of the Ising model on tree-like graphs

2024/10/29 by Hansen, Ulrik Thinggaard, Klausen, Frederik Ravn, Wildemann, Peter · 1 citation
#05C80 #60K35 #82B05 82B20 #82B26 #82B43 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2410.22061

Abstract

We consider the graphical representations of the Ising model on tree-like graphs. We construct a class of graphs on which the loop O(1) model and the single random current exhibit a non-unique phase transition with respect to the inverse temperature, highlighting the non-monotonicity of both models. It follows from the construction that there exist infinite graphs \mathbbG⊆ \mathbbG' such that the uniform even subgraph of \mathbbG' percolates and the uniform even subgraph of \mathbbG does not. We also show that on the wired d-regular tree, the phase transitions of the loop O(1), the single random current, and the random-cluster models are all unique and coincide.

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• A General Coupling for Ising Models and Beyond

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