MEM study of true flattening of free energy and the θ term

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.