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We investigate the nature of the chiral phase transition in the masslesstwo-flavor QCD using the renormalization group improved gauge action and theWilson quark action on $32^3\times 16$, $24^3\times 12$, and $16^3\times 8$lattices. Based on the renormalization group equation, we derive the scalingrelation for the effective masses of mesons at the chiral phase transitionpoint. If the chiral phase transition is second order, the effective masses asa function of the rescaled time/space do not depend on the lattice size andshow the universal behavior. We find that our numerical simulations on thethree sizes of lattices are excellently on the scaling curves, which isconsistent with the second order phase transition.

RG scaling relations at chiral phase transition in two-flavor QCD