We use the recently proposed directed-path algorithm to study the chiral limit of a strongly coupled lattice QCD with staggered quarks at finite temperatures. The new algorithm allows us to compute the chiral susceptibility and the pion decay constant accurately on large lattices for massless quarks. In the low temperature phase we find clear evidence for the singularities predicted by chiral perturbation theory. We also show convincingly that the chiral phase transition is of second order and belongs to the O(2) universality class.
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