Spontaneous scalarization phenomenon in scalar-tensor gravity is known to be a form of phase transition, and it was recently shown that the order of this transition changes depending on the parameters of the theory. There exists a phenomenological description of this result based on Landau theory, but the underlying mechanisms which determine the coefficients of the Landau expansion were unknown. In this study we calculate these coefficients starting from first principles. To this end, we start with an energy functional that describes the nonlinear behavior of the theory, and reduce it to an energy function. This allows us to explain the previously observed, but not well-understood, features of the scalarization phase transition, and enables us to predict which phase transition order will be present for which coupling function or in which regime of the parameter space. The details of the phase transition determine certain astrophysical observables such as signals sourced by transitions from metastable states in first-order scalarization. Thus, predicting these details is an important part of understanding scalarization itself.

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• Alternative gravity theories
• Phase transitions
• Neutron stars & pulsars