Integer optimization and zero temperature fixed point in Ising Random Field Systems.

Phase transition in a d = 3 ferromagnetic Ising model with random fields is analyzed directly at the zero-temperature critical point. The critical behavior is extracted from correlation functions averaged over an ensemble of exact ground states obtained with a new integer optimization algorithm. For Gaussian distribution of random fields finite-size scaling demonstrates a continuous phase transition with effective disconnected susceptibility exponent eta (bar) = -.9, correlation length exponent nu = 1.0 and magnetization exponent beta = .05, in agreement with recent scaling hypothesis.