In an excerpt from Finite-Size Scaling by John Cardy I found the following development:
At a first-order transition, the correlation length ξ remains finite, and the finite-size scaling properties in a truly finite geometry are quite simple if ξ << L. At the critical point there are two or more coexisting phases. If we label the mean values of the order parameter φ in these phases by φ1, φ2,... then we can write an effective probability distribution proportional to
$\sum_i exp(-{\frac{(φ-φ_i)^2}{2χ_i L^{-d}}})$
where χi, is the susceptibility in the ith pure phase.
which I can't manage to compute no matter what. My initial idea was to use something like Z = exp(-f/kbT), but I can't find the right expression for f.
Where does this formula come from?
