  The (111) surface of SnTe hosts one isotropic $\bar{\Gamma}$-centered and
three degenerate anisotropic $\bar{M}$- centered Dirac surface states. We
predict that a nematic phase with spontaneously broken $C_3$ symmetry will
occur in the presence of an external magnetic field when the $N=0$ $\bar{M}$
Landau levels are $1/3$ or $2/3$ filled. The nematic state phase boundary is
controlled by a competition between intravalley Coulomb interactions that favor
a valley-polarized state, and weaker intervalley scattering processes that
increase in relative strength with magnetic field. An in-plane Zeeman field
alters the phase diagram by lifting the three-fold $\bar{M}$ Landau level
degeneracy, yielding a ground state energy with $2\pi/3$ periodicity as a
function of Zeeman-field orientation angle.
