Scaling study of the two-flavor chiral phase transition with the Kogut-Susskind quark action in lattice QCD

Abstract

We report on a study of the two-flavor finite-temperature chiral phase transition employing the Kogut-Susskind quark action and the plaquette gluon action in lattice QCD for a lattice with ${N}_{t}=4$ temporal size. Hybrid $R$ simulations of ${10}^{4}$ trajectories are made at quark masses of ${m}_{q}=0.075,0.0375,0.02,0.01$ in lattice units for the spatial sizes ${8}^{3}{,12}^{3}$, and ${16}^{3}$. The spatial size dependence of various susceptibilities confirm the previous conclusion of the absence of a phase transition down to ${m}_{q}=0.02$. At ${m}_{q}=0.01$ an increase of susceptibilities is observed up to the largest volume ${16}^{3}$ explored in the present work. We argue, however, that this increase is likely to be due to an artifact of too small a lattice size and it cannot be taken to be the evidence for a first-order transition. Analysis of critical exponents estimated from the quark mass dependence of susceptibilities shows that they satisfy hyperscaling consistent with a second-order transition located at ${m}_{q}=0$. The exponents obtained from larger lattice, however, deviate significantly from both those of O(2), which is the exact symmetry group of the Kogut-Susskind action at finite lattice spacing, and those of O(4) expected from an effective $\ensuremath{\sigma}$ model analysis in the continuum limit.