  The critical behaviors of quark-hadron phase transition are explored by use
of the Ising model adapted for hadron production. Various measures involving
the fluctuations of the produced hadrons in bins of various sizes are examined
with the aim of quantifying the clustering properties that are universal
features of all critical phenomena. Some of the measures involve wavelet
analysis. Two of the measures are found to exhibit the canonical power-law
behavior near the critical temperature. The effect of final-state randomization
is studied by requiring the produced particles to take random walks in the
transverse plane. It is demonstrated that for the measures considered the
dependence on the randomization process is weak. Since temperature is not a
directly measurable variable, the average hadronic density of a portion of each
event is used as the control variable that is measurable. The event-to-event
fluctuations are taken into account in the study of the dependence of the
chosen measures on that control variable. Phenomenologically verifiable
critical behaviors are found and are proposed for use as a signature of
quark-hadron phase transition in relativistic heavy-ion collisions.
