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

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 $N_t=4\mathrm{}$ temporal size. Hybrid $R$ simulations of ${10}^4$ trajectories are made at quark masses of $m_q=0.075,0.0375,0.02,0.01\mathrm{}$ in lattice units for the spatial sizes $8^3{,12\mathrm{}}^3$, and ${16}^3$. The spatial size dependence of various susceptibilities confirm the previous conclusion of the absence of a phase transition down to $m_q=0.02\mathrm{}$. At $m_q=0.01\mathrm{}$ 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 $m_q=0\mathrm{}$. 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 $\sigma$ model analysis in the continuum limit.