MEM study of true flattening of free energy and the $\theta$ term

TL;DR

This paper investigates the effectiveness of the Maximum Entropy Method (MEM) in detecting genuine phase transitions in lattice field theories with a theta term, using mock data to simulate true flattening of free energy.

Contribution

It demonstrates how MEM can differentiate between false and true flattening of free energy in models with a theta term, aiding in understanding the sign problem.

Findings

MEM successfully detects true flattening in mock data.

Distinguishes between fictitious and genuine phase structure.

Provides insights into the sign problem in lattice field theory.

Abstract

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.