  We investigate the magnetization dynamics in nanomagnet vertices often found
in artificial spin ices. Our analysis involves creating a simplified model that
depicts edge magnetization using magnetic charges. We utilize the model to
explore the energy landscape, its associated curvatures, and the fundamental
modes. Our study uncovers specific magnonic regimes and transitions between
magnetization states, marked by zero-modes, which can be understood within the
framework of Landau theory. To verify our model, we compare it with
micromagnetic simulations, demonstrating a noteworthy agreement.
