Tricritical dynamics in $\mathrm{^3He}$-$\mathrm{^4He}$ mixtures and QCD

In this paper we study the universal critical dynamics near the tricritical points in $\mathrm{^3He}$-$\mathrm{^4He}$ mixtures and QCD with two massless quark flavors. In particular, we use the real-time formulation of the functional renormalization group to understand how the tricritical region connects the $O(4)$ Model G dynamics of the two-flavor chiral phase transition to that of Model H for the QCD critical point with explicitly broken chiral symmetry. We show that in presence of an additional subdiffusive energy-like density, the tricritical dynamics inherits the strong dynamic scaling of Model G, where the critical fluctuations of order parameter and conserved $O(N)$ charges relax at identical rates. The strong scaling in the planar $O(2)$ case relevant for the $\lambda$-line and the tricritical point in the liquid $\mathrm{^3He}$-$\mathrm{^4He}$ mixtures arises as an interesting limiting case. Including the explicit symmetry breaking by the finite light-quark masses in QCD, the energy-like density of the tricritical dynamics mixes linearly with the $Z_2$ order parameter to eventually produce the characteristic slow fluctuations of the entropy per baryon near the QCD critical point.