  In this paper we consider a class of (2+1)D schematic models with
four-fermion interactions that are effectively used in studying
condensed-matter systems with planar crystal structure, and especially
graphene. Symmetry breaking in these models occurs due to a possible appearance
of condensates. Special attention is paid to the symmetry properties of the
appearing condensates in the framework of discrete chiral and $\mathcal C$,
$\mathcal P$ and $\mathcal T$ transformations. Moreover, boundary conditions
corresponding to carbon nanotubes are considered and their relations with the
effect of an applied external magnetic field are studied. To this end we
calculated the effective potential for the nanotube model including effects of
finite temperature, density and an external magnetic field. As an illustration
we made numerical calculations of the chiral symmetry properties in a simpler
Gross--Neveu model with only one condensate taken into account. We also
investigated the phase structure of the nanotube model under the influence of
the Aharonov--Bohm effect and demonstrated that there is a nontrivial relation
between the magnitude of the Aharonov--Bohm phase, compactification of the
spatial dimension and thermal restoration of the originally broken chiral
symmetry.
