  We prove the sharp quantitative stability in the radial isotropic Almgren
problem. In addition, we develop a theory for estimating the sharp modulus in
the context of minimal assumptions on the surface tension and the potential and
obtain the sharp $\epsilon^2$ in any dimension. Inter-alia, we also solve the
problem of calculating the critical mass which was only a priori assumed to
exist and which breaks the mass regime into two sets: the one where the energy
is concave and the one where it is convex.
