Minor magnetization loops in two-dimensional dipolar Ising model

The two-dimensional dipolar Ising model is investigated for the relaxation and dynamics of minor magnetization loops. Monte Carlo simulations show that in a stripe phase an exponential decrease can be found for the magnetization maxima of the loops, M∼exp(−αNl) where Nl is the number of loops. We discuss the limits of this behavior and its relation to the equilibrium phase diagram of the model.