  Mapping quantum error correcting codes to classical disordered statistical
mechanics models and studying the phase diagram of the latter has proven a
powerful tool to study the fundamental error robustness and associated critical
error thresholds of leading quantum error correcting codes under
phenomenological noise models. In this work, we extend this mapping to admit
realistic, multi-parameter faulty quantum circuits in the description of
quantum error correcting codes. Based on the underlying microscopic circuit
noise model, we first systematically derive the associated strongly correlated
classical spin models. We illustrate this approach in detail for the example of
a quantum repetition code in which faulty stabilizer readout circuits are
periodically applied. Finally, we use Monte-Carlo simulations to study the
resulting phase diagram of the associated interacting spin model and benchmark
our results against a minimum-weight perfect matching decoder. The presented
method provides an avenue to assess the fundamental thresholds of QEC codes and
associated readout circuitry, independent of specific decoding strategies, and
can thereby help guiding the development of near-term QEC hardware.
