  Despite of simplicity of the transverse antiferromagnetic Ising model with a
uniform longitudinal field, its phases and involved quntum phase transitions
(QPTs) are nontrivial in comparison to its ferromagnetic counterpart. For
example, what is the nature of the mixed-order in such a model and does there
exist a disorder phase? Here we use a pattern picture to explore the
competitions between the antiferromagnetic Ising interaction, the transverse
and longitudinal fields and uncover what kind of pattern takes responsibility
of these three competing energy scales, thus determine the possible phases and
their QPTs or crossovers. Our results not only unveil rich physics of this
paradigmatic model, but also further stimulate quantum simulation by using
current available experimental platforms.
