Non trivial spacetime effects in a supersymmetric model

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.