EXACT DETERMINATION OF ALL GROUND-STATES OF RANDOM-FIELD SYSTEMS IN POLYNOMIAL-TIME

An algorithm is developed which allows calculating all ground states o f ferromagnetic and unfrustrated antiferromagnetic Ising systems with arbitrary site-dependent fields by transforming the system into an equ ivalent network and calculating the maximal flow. By a trial and error scheme a minimum cut is constructed which corresponds to a spin confi guration. In this way each ground state is calculated with a finite pr obability. The algorithm is applied to site-diluted antiferromagnets i n external magnetic fields. It is found that in this case its time com plexity is approximately quadratic in the lattice size. As an applicat ion we calculate the distribution of overlaps between ground states of the site-diluted antiferromagnet in a strong magnetic field and we an alyse the fractal structure of these ground states.