  A surface of a strong topological insulator (STI) is characterized by an odd
number of linearly dispersing gapless electronic surface states. It is well
known that such a surface cannot be described by an effective two-dimensional
lattice model (without breaking the time-reversal symmetry), which often
hampers theoretical efforts to quantitatively understand some of the properties
of such surfaces, including the effect of strong disorder, interactions and
various symmetry-breaking instabilities. Here we formulate a lattice model that
can be used to describe a {\em pair} of STI surfaces and has an odd number of
Dirac fermion states with wavefunctions localized on each surface. The
Hamiltonian consists of two planar tight-binding models with spin-orbit
coupling, representing the two surfaces, weakly coupled by terms that remove
the extra Dirac points from the low-energy spectrum. We illustrate the utility
of this model by studying the magnetic and exciton instabilities of the STI
surface state driven by short-range repulsive interactions and show that this
leads to results that are consistent with calculations based on the continuum
model as well as three-dimensional lattice models. We expect the model
introduced in this work to be widely applicable to studies of surface phenomena
in STIs.
