Two-dimensional Ising model with competing interactions: phase diagram and low-temperature remanent disorder

The two-dimensional Ising model with competing nearest-neighbor and diagonal interactions on the square lattice is studied by the transfer-matrix technique and by the Monte Carlo simulations. The phase diagram of this model is constructed with a special emphasis to the analysis of a glassy state arising as an order to disorder transition at low temperatures. Evidence of the glassy state (based, in particular, on the calculation of the average length of domain walls and on the Edwards-Anderson order parameter) and its characteristics are presented. It was shown that, in the frustrated Ising model, the domain-wall length correlates to the onset of the glassy state, that is, it may play the role of the order parameter for the Ising glass or for glasslike states in other frustrated magnetic systems.