Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential

TL;DR

It is demonstrated that the shape of the deconfinement critical line for real chemical potentials is dictated by tricritical scaling and implies the weakening of thedeconfinement transition with realchemical potential.

Abstract

We present unambiguous evidence from lattice simulations of QCD with three degenerate quark species for two tricritical points in the (T,m) phase diagram at fixed imaginary μ/T=iπ/3 mod 2π/3, one in the light and one in the heavy mass regime. These represent the boundaries of the chiral and deconfinement critical lines continued to imaginary chemical potential, respectively. It is demonstrated that the shape of the deconfinement critical line for real chemical potentials is dictated by tricritical scaling and implies the weakening of the deconfinement transition with real chemical potential. The generalization to non-degenerate and light quark masses is discussed.

Figures (5)

• Figure 1: Left: phase diagram for imaginary $\mu$. Vertical lines are first order transitions between different $Z(3)$-sectors, arrows indicate the phase of the Polyakov loop. The $\mu=0$ chiral/deconfinement transition continues to imaginary chemical potential, its order depends on $N_f$ and the quark masses. Right: phase diagram for $N_f=3$ at fixed $\mu=i\pi T$. Solid lines are lines of triple points ending in tricritical points, which are connected by a $Z(2)$-line.
• Figure 2: Finite size scaling of $B_4$ for a small quark mass. On the right, the critical exponent was fixed to $\nu=1/3$, corresponding to a first order transition.
• Figure 3: Left: Critical exponent $\nu$ at $\mu/T=i\pi$. Right: Distribution of ${\rm Im}(L)$ at the endpoint of the $Z(3)$ transition.
• Figure 4: Order of the transition as a function of quark masses. Left: quark hadron transition at $\mu=0$. Right: the $Z(3)$-transition endpoint at $\mu/T=i\pi/3$.
• Figure 5: Critical line $m_c(\mu^2)$ in the 3-state Potts model fkt (left) and for QCD in a strong coupling expansion lp (right).