True or Fictitious Flattening? -MEM and the $θ$ Term-

Abstract

We study the sign problem in lattice field theory with a $θ$ term. We apply the maximum entropy method (MEM) to flattening phenomenon of the free energy density $f(θ)$, which originates from the sign problem. In our previous paper, we applied the MEM by employing the Gaussian topological charge distribution $P(Q)$ as mock data. In the present paper, we consider models in which `true' flattening of $f(θ)$ occurs. These may be regarded as good examples for studying whether the MEM could correctly detect non trivial phase structure.