Significance The ϵ expansion around the upper critical dimension is a standard tool for studying critical phenomena of models defined on finite-dimensional lattices. However, it faces problems in describing strongly disordered models. Here we use a loop expansion around the Bethe solution, an advanced mean-field theory, since it provides a complete description of the fluctuations that play an important role at low temperatures, especially at finite connectivity. We study the random-field Ising model, a prototypical strongly disordered model, via this loop expansion. We find indeed additional correcting terms in the correlation functions at the one-loop order, but these are subdominant with respect to those coming from the standard ϵ expansion that is then correct at this order.