next subsection, we consider a different noise process on the $|\psi _+\ra $ where the coherence of the model is mapped to order parameter of random bond Ising model.

Random bond Ising model and transition in coherence
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Let us start again with the initial state $|\psi_+ \ra$. Then, we consider two sequences of bit-flip channels of (\[bit\]) where the probability of the noise is $p$ for the first channel and is $q$ for the second one. We also suppose that after the first quantum channel, a measurement of face operators $B_F$ is done in order to find what excitations have been generated by the noise. Therefore, after measurement we will have a quenched pattern of the error and then the second quantum channel is applied. Consequently, the final quantum state should be in the following form: $$\label{bit1}
\Phi[\boldsymbol\eta] =\sum_{\mathcal{E}} W_{\mathcal{E}}(q) \hat{\mathcal{E}}(X) \hat{\eta}(X) |\psi_+ \ra \la \psi _+| \hat{\eta}(X)\hat{\mathcal{E}}(X),$$ where $\eta$ refers to the error pattern generated by the first channel. Similar to the previous subsection, here we give a geometrical description of the above state. The most important difference is that here we have a combination of two noise patterns related to operators $\hat{\mathcal{E}}(X)$ and $ \hat{\eta}(X)$. However, both 