We make a numerical study of hysteresis loop shapes within a generalized two-dimensional Random Anisotropy Nematic (RAN) model at zero temperature. The hysteresis loops appear on cycling a static external ordering field. Ordering in these systems is history dependent and involves interplay between the internal coupling constant J, the anisotropy random field D, and the ordering external field H. Here the external field is represented by a traceless tensor, analogous to extension-type fields in continuum mechanics. The calculations use both a mean field approach and full lattice simulations. Our analysis suggests the existence of two qualitatively different solutions, which we denote as symmetric and symmetry breaking. For the set of parameters explored, only the symmetric solutions are stable. Both approaches yield qualitatively similar hysteresis curves, which are manifested either by single or double loops. But the quantitative differences indicate that mean field estimates are only of limited predictive value.
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