Computer simulations of a two-dimensional system with competing interactions.

The results and methodology of large scale computer simulations of the two-dimensional dipolar Ising model with long-range interactions are reported. Systems as large as 117,649 particles were studied to elucidate the elementary excitations and phase diagram of two-dimensional systems, such as Langmuir monolayers, thin garnet films, and adsorbed films on solid surfaces, which spontaneously form patterns of stripes, bubbles, and intermediately shaped domains. The challenging numerical investigations of large scale systems with long-range interactions at low temperatures were made possible by combining the fast multipole method and a non-Metropolis Monte Carlo sampling technique. Our simulations provide evidence that, at sufficiently high ratios of the repulsive to the attractive coupling constant for the model, twofold stripe order in the systems of interest is lost through a defect-mediated mechanism. Heat capacity data and the excitations observed in our simulations as the system disorders indicate that it is most likely an instance of a Kosterlitz-Thouless phase transition. The results from simulations with and without external field are in excellent agreement with the predictions of an analytic scaling theory [A. D. Stoycheva and S. J. Singer, Phys. Rev. E 64, 016118 (2001)], confirming the phase diagram furnished by the analytic model. The scaling theory suggests that, under certain conditions, defect-mediated stripe melting may be supplanted by Ising like disordering within stripes for small repulsion strength. A qualitative discussion of a model that supports both disordering mechanisms is presented.