Ground-state magnetization of Ising spin glasses

We study the magnetization of the ground states of Ising spin glasses as a function of the magnetic field. The grids are two-dimensional with Gaussian bond distribution. Finding a ground state in this case is a difficult combinatorial problem. We present a method that guarantees finding a true ground state. Although it is unlikely that one can have an algorithm with a polynomial bound for the running time, in all cases we tried, our method found a solution in a reasonable amount of time. We used this to obtain estimations of the critical exponents.