We use local adiabatic evolution to experimentally create and determine the ground-state spin ordering of a fully connected Ising model with up to 14 spins. Local adiabatic evolution-in which the system evolution rate is a function of the instantaneous energy gap-is found to maximize the ground-state probability compared with other adiabatic methods while requiring knowledge only of the lowest similar to N of the 2(N) Hamiltonian eigenvalues. We also demonstrate that the ground-state ordering can be experimentally identified as the most probable of all possible spin configurations, even when the evolution is highly nonadiabatic.