We study the sign problem in lattice field theory with a $theta$ term, which reveals as flattening phenomenon of the free energy density $f(theta)$. We report the result of the MEM analysis, where such mock data are used that `true flattening of $f(theta)$ occurs. This is regarded as a simple model for studying whether the MEM could correctly detect non trivial phase structure in $theta$ space. We discuss how the MEM distinguishes fictitious and true flattening.
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