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We return to the question of how the choice of stabilizer generators affectsthe preservation of information on structures whose degenerate ground stateencodes a classical redundancy code. Controlled-not gates are used to transformthe stabilizer Hamiltonian into a Hamiltonian consisting of uncoupled singlespins and/or pairs of spins. This transformation allows us to obtain ananalytical partition function and derive closed form equations for the relativemagnetization and susceptibility. These equations are in agreement with thenumerical results presented in [arXiv:0907.0394v1] for finite size systems.Analytical solutions show that there is no finite critical temperature, Tc=0,for all of the memory structures in the thermodynamic limit. This is incontrast to the previously predicted finite critical temperatures based onextrapolation. The mismatch is a result of the infinite system being a poorapproximation even for astronomically large finite size systems, wherespontaneous magnetization still arises below an apparent finite criticaltemperature. We extend our analysis to the canonical stabilizer Hamiltonian.Interestingly, Hamiltonians with two-body interactions have a higher apparentcritical temperature than the many-body Hamiltonian.

Analytical solution of thermal magnetization on memory stabilizer structures