  In this paper we study the effect of dependence on detecting a class of
structured signals in Ferromagnetic Ising models. Natural examples of our class
include Ising Models on lattices, and Mean-Field type Ising Models such as
dense Erd\H{o}s-R\'{e}nyi, and dense random regular graphs. Our results not
only provide sharp constants of detection in each of these cases and thereby
pinpoint the precise relationship of the detection problem with the underlying
dependence, but also demonstrate how to be agnostic over the strength of
dependence present in the respective models.
