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تسجيل مستخدم جديدTrue or Fictitious Flattening? -MEM and the $theta$ Term-
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We study the sign problem in lattice field theory with a $theta$ term. We apply the maximum entropy method (MEM) to flattening phenomenon of the free energy density $f(theta)$, 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 $f(theta)$ occurs. These may be regarded as good examples for studying whether the MEM could correctly detect non trivial phase structure.
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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 $f(t
heta)$ 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.
Lattice field theory with the $theta$ term suffers from the sign problem. The sign problem appears as flattening of the free energy. As an alternative to the conventional method, the Fourier transform method (FTM), we apply the maximum entropy me
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In Monte Carlo simulations of lattice field theory with a $theta$ term, one confronts the complex weight problem, or the sign problem. This is circumvented by performing the Fourier transform of the topological charge distribution $P(Q)$. This proced
ure, however, causes flattening phenomenon of the free energy $f(theta)$, which makes study of the phase structure unfeasible. In order to treat this problem, we apply the maximum entropy method (MEM) to a Gaussian form of $P(Q)$, which serves as a good example to test whether the MEM can be applied effectively to the $theta$ term. We study the case with flattening as well as that without flattening. In the latter case, the results of the MEM agree with those obtained from the direct application of the Fourier transform. For the former, the MEM gives a smoother $f(theta)$ than that of the Fourier transform. Among various default models investigated, the images which yield the least error do not show flattening, although some others cannot be excluded given the uncertainty related to statistical error.
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