Probing the Aoki phase with N_f=2 Wilson fermions at finite temperature

TL;DR

This study investigates the existence and characteristics of the Aoki phase at finite temperature using Wilson fermions, confirming its presence at specific parameters but facing challenges in distinguishing it from thermal transitions.

Contribution

First numerical confirmation of the Aoki phase at finite temperature with Wilson fermions, extending previous zero-temperature studies and exploring phase boundaries.

Findings

Aoki phase exists at finite temperature near certain $eta$ and $\kappa$ values.

The Aoki phase is shifted to lower $\kappa$ compared to zero temperature.

Thermal transition line could not be separated from the Aoki phase despite fine-tuning.

Abstract

In this letter we report on a numerical investigation of the Aoki phase in the case of finite temperature which continues our former study at zero temperature. We have performed simulations with Wilson fermions at $\beta=4.6$ using lattices with temporal extension $N_{\tau}=4$. In contrast to the zero temperature case, the existence of an Aoki phase can be confirmed for a small range in $\kappa$ at $\beta=4.6$, however, shifted slightly to lower $\kappa$. Despite fine-tuning $\kappa$ we could not separate the thermal transition line from the Aoki phase.