  We calculate the critical temperature of the Ising model on a set of graphs
representing a concatenated three-bit error-correction code. The graphs are
derived from the stabilizer formalism used in quantum error correction. The
stabilizer for a subspace is defined as the group of Pauli operators whose
eigenvalues are +1 on the subspace. The group can be generated by a subset of
operators in the stabilizer, and the choice of generators determines the
structure of the graph. The Wolff algorithm, together with the histogram method
and finite-size scaling, is used to calculate both the critical temperature and
the critical exponents of each structure. The simulations show that the choice
of stabilizer generators, both the number and the geometry, has a large effect
on the critical temperature.
