Nonmagnetic impurity effects of the spin disordered state in the triangular antiferromagnet NiGa$_2$S$_4$ was studied through magnetic and thermal measurements for Ni$_{1-x}$Zn$_x$Ga$_2$S$_4$ (0.0le xle 0.3). Only 1 % substitution is enough to strongly suppress the coherence observed in the spin disordered state. However, the suppression is not complete and the robust feature of the T^2 dependent specific heat and its scaling behavior with the Weiss temperature indicate the existence of a coherent Nambu-Goldstone mode. Absence of either conventional magnetic order or bulk spin freezing suggests a novel symmetry breaking of the ground state.
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