Detailed structure of configuration space and its importance on ergodic separation of ±J Ising lattices

A complete and exact characterization of the configuration space of 2-D ±J Ising lattices is performed. A new algorithm is introduced here representing advantages for reaching all states for small samples and doing a non-biased sampling of ground states for larger samples. We report efficient procedures to find all ground states grouped in local ensembles of ground states (LEGs) and also a convenient way of storing and comparing states. Properties of such LEGs differ from some approximate descriptions reported in the literature. The onset of lattice size dependence of properties is discussed. Four different ways of performing ergodic separation are used to calculate order parameters. The most significant way of doing ergodic separation requires previous classification of states in LEGs.