Two-dimensional magnetic garnets exhibit complex and fascinating magnetic
domain structures, like stripes, labyrinths, cells and mixed states of stripes
and cells. These patterns do change in a reversible way when the intensity of
an externally applied magnetic field is varied. The main objective of this
contribution is to present the results of a model that yields a rich pattern
structure that closely resembles what is observed experimentally. Our model is
a generalized two-dimensional Ising-like spin-one Hamiltonian with long-range
interactions, which also incorporates anisotropy and Zeeman terms. The model is
studied numerically, by means of Monte Carlo simulations. Changing the model
parameters stripes, labyrinth and/or cellular domain structures are generated.
For a variety of cases we display the patterns, determine the average size of
the domains, the ordering transition temperature, specific heat, magnetic
susceptibility and hysteresis cycle. Finally, we examine the reversibility of
the pattern evolution under variations of the applied magnetic field. The
results we obtain are in good qualitative agreement with experiment.Comment: 8 pages, 12 figures, submitted to Phys. Rev.