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We show several calculations to identify the critical point in the groundstate in random spin systems including spin glasses on the basis of the dualityanalysis. The duality analysis is a profound method to obtain the preciselocation of the critical point in finite temperature even for spin glasses. Wepropose a single equality for identifying the critical point in the groundstate from several speculations. The equality can indeed give the exactlocation of the critical points for the bond-dilution Ising model on severallattices and provides insight on further analysis on the ground state in spinglasses.

A challenge for critical point of spin glass in ground state