Phase transition in finite density and temperature lattice QCD

TL;DR

This paper studies the phase transition in lattice QCD at finite temperature and chemical potential by analyzing the behavior of the chiral condensate and its derivatives, revealing significant second-order effects near the transition.

Contribution

It introduces a Taylor expansion approach to compute derivatives of the chiral condensate in lattice QCD at finite density and temperature, providing new insights into phase transition behavior.

Findings

Second derivatives of the chiral condensate are sizable near the phase transition.

Finite chemical potential decreases the magnitude of the chiral condensate.

First derivatives are small, indicating subtle initial changes in the condensate.

Abstract

We investigate the behavior of the chiral condensate in lattice QCD at finite temperature and finite chemical potential. The study was done using two flavors of light quarks and with a series of $\beta$ and $ma$ at the lattice size $24\times12^{2}\times6$. The calculation was done in the Taylar expansion formalism. We are able to calculate the first and second order derivatives of $\langle\bar{\psi}\psi\rangle$ in both isoscalar and isovector channels. With the first derivatives being small, we find that the second derivatives are sizable close to the phase transition and the magnitude of $\bar{\psi}\psi$ decreases under the influence of finite chemical potential in both channels.