Lee–Yang zero avoidance for recursive Ising models

Determine whether, for every non-degenerate and expanding graph recursion operator R and every fixed ferromagnetic parameter b∈(0,1), the Lee–Yang zeros of the Ising-model partition functions Z_{G_n}(λ,b) avoid a uniform neighborhood of λ=1 along every recursively generated graph sequence.

Background

The paper’s dynamical method is motivated as potentially applicable to other statistical-mechanical partition functions. For the ferromagnetic Ising model, general bounded-degree results give zero avoidance near λ=1 only above a model-dependent threshold in the temperature parameter b; recursive graph structure might yield zero avoidance even below that threshold.

References

Is it true that, in the ferromagnetic Ising model, for all fixed b∈(0,1) the Lee--Yang zeros of Z_{G_n} avoid a uniform neighborhood of λ=1?

— Zeros of the independence polynomial on recursive sequences of graphs  (2609.35102 - Hlushchanka et al., 28 Sep 2026) in Section 1, subsection “Open questions,” subsubsection “Other partition functions”

It is therefore not clear whether the arguments in Section~\ref{section: zeros} generalize to the random setting, as these rely crucially on the fixed-point structure of M_0, which is lost when the recursion operator varies randomly.

— Zeros of the independence polynomial on recursive sequences of graphs  (2609.35102 - Hlushchanka et al., 28 Sep 2026) in Section 1, subsection “Open questions,” subsubsection “Random recursive graphs”