Deterministic equivalent for the Allen-Cahn energy of a scaling law in the Ising model

For the Allen-Cahn functional we study the following problem: for which prescribed amount m of volume is there the appearence of a droplet of one phase inside the other? Under a suitable assumption on the domain we show that the breaking of symmetry occurs at the same value of m as for the limit of the sharp interface energy. We also prove that there exists a threshold for m of order epsilon(n/n+1) so that either there is the appearence of the droplet or there is no breaking of symmetry.