  We study the four-dimensional Z_2 random-plaquette lattice gauge theory as a
model of topological quantum memory, the toric code in particular. In this
model, the procedure of quantum error correction works properly in the ordered
(Higgs) phase, and phase boundary between the ordered (Higgs) and disordered
(confinement) phases gives the accuracy threshold of error correction. Using
self-duality of the model in conjunction with the replica method, we show that
this model has exactly the same mathematical structure as that of the two
dimensional random-bond Ising model, which has been studied very extensively.
This observation enables us to derive a conjecture on the exact location of the
multicritical point (accuracy threshold) of the model, p_c=0.889972..., and
leads to several nontrivial results including bounds on the accuracy threshold
in three dimensions.
