Effects of the Anomaly on the Two-Flavor QCD Chiral Phase Transition

We use strongly coupled lattice QED with two flavors of massless staggered fermions to model the chiral phase transition in two-flavor massless QCD. Our model allows us to vary the QCD anomaly and thus study its effects on the transition. Our study confirms the widely accepted viewpoint that the chiral phase transition is first order in the absence of the anomaly. Turning on the anomaly weakens the transition and turns it second order at a critical anomaly strength. The anomaly strength at the tricritical point is characterized using $r=(M_{{\eta }^{\prime }}-M_{\pi })/{\rho }_{{\eta }^{\prime }}$, where $M_{{\eta }^{\prime }}$, $M_{\pi }$ are the screening masses of the anomalous and regular pions and ${\rho }_{{\eta }^{\prime }}$ is the mass scale that governs the low energy fluctuations of the anomalous symmetry. We estimate that $r\sim 7$ in our model. This suggests that a strong anomaly at the two-flavor QCD chiral phase transition is necessary to wash out the first order transition.

Figure 1

An example of a DPI configuration in two dimensions.

Figure 2

Plot of $L{Y}_A$ and $L{Y}_C$ versus $T$ for different values of $L$ for $C=0$. The lack of a point where all the curves cross shows the absence of a second order transition. We can estimate $T_c\sim 2.466(1)$.

Figure 3

Plot of $L{Y}_C$ versus $T$ for different values of $L$ for $C=0.3$. The presence of a point where all the curves cross shows the presence of a second order transition. We can estimate $T_c=2.83555(10)$. The inset shows that all our data fit $O(4)$ scaling extremely well.

Figure 4

Plot of $L{Y}_C$ (top) and $\chi /L^2$ (bottom) versus $T$ for different values of $L$ for $C=0.03$. The scaling of $\chi$ assumes $\eta =0$. The presence of a point where all the curves cross shows the presence of a second order transition. We can estimate $T_c\sim 2.52652(3)$.

Figure 5

The plots shown are close to the tricritical point $C=0.03$ and $T=2.5265$. Assuming $\nu =0.5$ and $\eta =0$, in the top panel we show $L{Y}_C$ and $\chi /L^{2-\eta }$ as a function of $(T-T_c)L^{1/\nu }$ for all of our data. The fact that all the data fall on a single curve demonstrates mean field universality. The bottom-left panel is the plot of $Y_A$ versus $L$ and the right panel shows the correlation function $G(x)$. Solid lines are fits discussed in the text.