Universality of the critical point mapping between Ising model and QCD at small quark mass

Abstract

The universality of the QCD equation of state near the critical point is expressed by mapping pressure as a function of temperature T and baryon chemical potential µ in QCD to Gibbs free energy as a function of reduced temperature r and magnetic field h in the Ising model. The mapping parameters are, in general, not universal, i.e., determined by details of the microscopic dynamics, rather than by symmetries and long-distance dynamics. In this paper we point out that in the limit of small quark masses, when the critical point is close to the tricritical point, the mapping parameters show universal dependence on the quark mass mq. In particular, the angle between the r = 0 and h = 0 lines in the (µ, T ) plane vanishes as m 2/5 q . We discuss possible phenomenological consequences of these findings.1 These considerations would also apply, mutatis mutandis, to the tricritical point separating the second and first-order transitions as a function of the strange quark mass [5,6], instead of the baryon chemical potential.

Critical behavior of the bulk viscosity in QCD

“…(7). It was recently observed that close to the chiral limit this assumption is not correct, and that in models of QCD this observation also applies to realistic values of the quark masses [45]. To illustrate this fact we show in Fig.…”

Machine learning phase transitions of the three-dimensional Ising universality class

“…along the direction of line (iii), the transition will be a smooth crossover. According to a non-universal mapping between Ising variables (t, H) and QCD coordinates (T, µ B ) in the phase diagrams, we can construct an equation of state matching the first principle Lattice QCD calculations, which can be employed in hydrodynamic simulations in relativistic heavy-ion collision [32][33][34][35].…”

“…Therefore, universality makes the Ising model very relevant for studies of systems that display the Z(2) symmetry [28][29][30][31]. By means of a parametrization of the scaling equation of state in the 3D Ising model and a non-universal mapping, it allows to construct an equation of state matching the first principle Lattice QCD calculations and to include the proper scaling behavior in the proximity of the CP [11,[32][33][34][35]. It can also map the phase diagram of the 3D Ising model onto the one of QCD [32,36,37].…”

“…By means of a parametrization of the scaling equation of state in the 3D Ising model and a non-universal mapping, it allows to construct an equation of state matching the first principle Lattice QCD calculations and to include the proper scaling behavior in the proximity of the CP [11,[32][33][34][35]. It can also map the phase diagram of the 3D Ising model onto the one of QCD [32,36,37]. Thus the CP, the lines of first-order phase transition and crossover in the 3D Ising model are related to those of QCD.…”

Charting the scaling region of the Ising universality class in two and three dimensions

“…In particular it is widely expected that the hadronic phase (low T, low μ) should be separated from the quark-gluon plasma phase (high T, high μ) by a line of first order transitions with a critical end point at finite critical values of T and μ (see Fig. 5) which should again belong to the Ising universality class [58][59][60][61][62][63][64][65].…”