  We investigate the low-energy spectral properties and robustness of the
topological phase of color code, which is a quantum spin model for the aim of
fault-tolerant quantum computation, in the presence of a uniform magnetic field
or Ising interactions, using high-order series expansion and exact
diagonalization. In a uniform magnetic field, we find 1st-order phase
transitions in all field directions. In contrast, our results for the Ising
interactions unveil that for strong enough Ising couplings, the Z2 x Z2
topological phase of color code breaks down to symmetry broken phases by 1st-
or 2nd-order phase transitions.
