The Sign Problem and MEM in Lattice Field Theory with the Term

Lattice field theory with a $\theta$ term suffers from the sign problem. The sign problem appears as flattening of the free energy. As an alternative way to the conventional method, the Fourier transform method (FTM), we apply the maximum entropy method (MEM) to Monte Carlo data of the CP$^3$ model with the $\theta$ term. For the data without flattening, we obtain the most probable images of the partition function ${\hat{\cal Z}}(\theta)$ with rather small errors, which are almost in agreement with the result of the FTM. Based upon this, we systematically investigate flattening in terms of the MEM