  Monolayer graphene at charge neutrality in a quantizing magnetic field is a
quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there
is a plethora of possible ground states. Previous theoretical work, based on a
stringent ultra short-range assumption on the symmetry-allowed interactions,
predicts a phase diagram with distinct regions of spin-polarized, canted
antiferromagnetic, inter-valley coherent, and charge density wave order. While
early experiments suggested that the system was in the canted antiferromagnetic
phase at a perpendicular field, recent scanning tunneling studies universally
find Kekul\'e bond order, and sometimes also charge density wave order.
Recently, it was found that if one relaxes the stringent assumption mentioned
above, a phase with coexisting canted antiferromagnetic and Kekul\'e order
exists in the region of the phase diagram believed to correspond to real
samples. In this work, starting from the continuum limit appropriate for
experiments, we present the complete phase diagram of $\nu=0$ graphene in the
Hartree-Fock approximation, using generic symmetry-allowed interactions,
assuming translation invariant ground states up to an intervalley coherence.
Allowing for a sublattice potential (valley Zeeman coupling), we find numerous
phases with different types of coexisting order. We conclude with a discussion
of the physical signatures of the various states.
