Efficient Algorithm for Finding Ground-States in the Random Field Ising Model with an External Field

We present an efficient algorithm that, combined with a max-flow, min-cut minimization algorithm, makes it possible to find the ground states of the Gaussian Random Field Ising model when the external applied field B is continuously varied from −∞ to +∞. The algorithm exactly finds all the possible ground states and their limiting range (Bmin, Bmax). Examples of the dependence of the magnetization and energy with B are shown for the 2d-RFIM.