Determine whether bounded external field is necessary

Determine whether the constant upper bound on the uniform external field \(\lambda\) is inherent to approximating the partition function of antiferromagnetic Ising models on random regular bipartite graphs or is merely a limitation of the current analytical methods.

Background

The main theorem requires $\lambda$ to be bounded by a constant. The authors explain that this assumption is important in their current analysis because it supports the concentration estimates used to identify suitable truncation parameters and analyze conditioned configuration spaces. They nevertheless leave unresolved whether this restriction reflects a genuine barrier for approximation or only the limitations of the proof techniques developed in the paper.