  Ground-state phase diagram of the toric code model in a parallel magnetic
field has three distinct phases: topological, charge-condensed, and
vortex-condensed states. To study it we consider an implicit local order
parameter characterizing the transition between the topological and
charge-condensed phases, and sample it using continuous-time Monte Carlo
simulations. The corresponding second-order transition line is obtained by
finite-size scaling analysis of this order parameter. Symmetry breaking between
charges and vortices along the first-order transition line is also observed,
and our numerical result shows that the end point of the first-order transition
line is located at $h_x^{(c)}=h_z^{(c)}=0.418(2)$.
