Magnetic equation of state in (2+1)-flavor QCD

Abstract

A first study of critical behavior in the vicinity of the chiral phase transition of ($2+1$)-flavor QCD is presented. We analyze the quark mass and volume dependence of the chiral condensate and chiral susceptibilities in QCD with two degenerate light quark masses and a strange quark. The strange quark mass (${m}_{s}$) is chosen close to its physical value; the two degenerate light quark masses (${m}_{l}$) are varied in a wide range $1/80\ensuremath{\le}{m}_{l}/{m}_{s}\ensuremath{\le}2/5$, where the smallest light quark mass value corresponds to a pseudoscalar Goldstone mass of about 75 MeV. All calculations are performed with staggered fermions on lattices with temporal extent ${N}_{\ensuremath{\tau}}=4$. We show that numerical results are consistent with $O(N)$ scaling in the chiral limit. We find that in the region of physical light quark mass values, ${m}_{l}/{m}_{s}\ensuremath{\simeq}1/20$, the temperature and quark mass dependence of the chiral condensate is already dominated by universal properties of QCD that are encoded in the scaling function for the chiral order parameter, the magnetic equation of state. We also provide evidence for the influence of thermal fluctuations of Goldstone modes on the chiral condensate at finite temperature. At temperatures below, but close to the chiral phase transition at vanishing quark mass, this leads to a characteristic dependence of the light quark chiral condensate on the square root of the light quark mass.