  We have studied the properties of biaxial particles interacting via an
anisotropic pair potential, involving second rank quadrupolar and third rank
octupolar coupling terms, using Monte Carlo simulation. The particles occupy
the sites of a 2D square lattice and the interactions are restricted to nearest
neighbours. The system exhibits spontaneous chiral symmetry breaking from an
isotropic phase to a chiral modulated nematic phase, composed of ambidextrous
chiral domains. When two-fold axes of quadrupolar and octupolar tensors
coincide this modulated phase appears to be the ambidextrous cholesteric phase
of pitch comparable with a few lattice spacings, which can be regarded as a
limiting case of the nematic twist bend phase. The associated phase transition
is first-order.
