The effective potential as an energy density: The one phase region

An explicit formula is given relating the effective potential in a finite volumeP()₂ quantum field theory to the expected energy density under the constraint of a fixed average filed. In the one phase region, i.e., where the classical potential equals its convex hull and has nonvanishing second derivative, it is shown via a central limit theorem that in the infinite volume limit the effective potential is equal to the constrained energy density, provided is sufficiently small.