  In this paper, we study the effect of dependence on detecting a class of
signals in Ising models, where the signals are present in a structured way.
Examples include Ising Models on lattices, and Mean-Field type Ising Models
(Erd\H{o}s-R\'{e}nyi, Random regular, and dense graphs). Our results rely on
correlation decay and mixing type behavior for Ising Models, and demonstrate
the beneficial behavior of criticality in the detection of strictly lower
signals. As a by-product of our proof technique, we develop sharp control on
mixing and spin-spin correlation for several Mean-Field type Ising Models in
all regimes of temperature -- which might be of independent interest.
