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We compute the structure factor of the $J_1$-$J_2$ Ising model in an externalfield on the square lattice within the Cluster Variation Method. We use a fourpoint plaquette approximation, which is the minimal one able to capture phaseswith broken orientational order in real space, like the recently reportedIsing-nematic phase in the model. The analysis of different local maxima in thestructure factor allows us to track the different phases and phase transitionsagainst temperature and external field. Although the nematic susceptibility isnot directly related to the structure factor, we show that because of the closerelationship between the nematic order parameter and the structure factor, thelatter shows unambiguous signatures of the presence of a nematic phase, inagreement with results from direct minimization of a variational free energy.The disorder variety of the model is identified and the possibility that theCVM four point approximation be exact on the disorder variety is discussed.

Pair correlations and structure factor of the $J_1$-$J_2$ square lattice Ising model in an external field within the Cluster Variation Method