  We study a ${N=1}$ supersymmetric model in a ${S}^{1}{\times R}^{3}$
spacetime. We find that by choosing appropriate boundary conditions for the
contributing fields supersymmetry can be preserved. However if we add a hard
supersymmetry breaking term, we observe that for small values of the length of
the ${S}^{1}$ dimension, supersymmetry remains unbroken and breaks
spontaneously when the length exceeds a critical value. The final picture
resembles the first order phase transition picture.
