Maximum Entropy Method Approach to the   Term

Abstract

In Monte Carlo simulations of lattice field theory with a θ 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 procedure, however, causes flattening phenomenon of the free energy f (θ), 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 θ 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 (θ) 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. * )

Application of maximum entropy method to lattice field theory with a topological term

“…The result is free from the flattening and consistent with Z pois (θ). Hence we conclude that the MEM works for the θ term and reproduces the reasonable image [ 10]. …”

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

“…This is in contrast to the case of fictitious flattening studied in (I), where the MEM could predict no fictitious flattening [4]. Applicability of the MEM associated with the magnitude of the errors in P (Q) will be reported elsewhere.…”

Lattice Field Theory with the Sign Problem and the Maximum Entropy Method

“…In the present talk, we review the analysis of the sign problem based on the maximum entropy method (MEM) [1,2,3]. For details, refer to [4,5,6]. The MEM is well known as a powerful tool for so-called ill-posed problems, where the number of parameters to be determined is much larger than the number of data points.…”