The \({J}_{1}-{J}_{2}\) frustrated two-dimensional Ising antiferromagnet in the magnetic fields on the square lattice is studied using a functional integral method. First, we determine possible ground states of the model including Néel antiferromagnetic phase and striped antiferromagnetic phase, which depend on the value of the frustrated parameter \(\alpha ={J}_{2}/{J}_{1}\) . The influence of the spin fluctuations in the presence of the frustration, temperature, and longitudinal and transverse fields on these two phases is also studied, which shows the strong impact of the spin fluctuations at the phase transition points. The effects of the longitudinal and transverse fields are highlighted. In addition, we also calculate and plot the temperature dependence of the magnetic susceptibility, and we find a sharp peak related to a phase transition and a rounded peak related to the competition of the effects of the antiferromagnetic exchange couplings, temperature and fields. Hence, we suggest experimental relevance for the given theoretical model with Li2VOSiO4 and YbBi2IO4.
