  We report on a study of 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 sigma model
analysis in the continuum limit.
