We provide necessary and sufficient conditions for freezing of quantumcorrelations as measured by quantum discord and quantum work deficit in thecase of bipartite as well as multipartite states subjected to local noisychannels. We recognize that inhomogeneity of the magnetizations of the sharedquantum states plays an important role in the freezing phenomena. We show thatthe frozen value of the quantum correlation and the time interval for freezingfollow a complementarity relation. For states which do not exhibit "exact"freezing, but can be frozen "effectively", by having a very slow decay ratewith suitable tuning of the state parameters, we introduce an index -- thefreezing index -- to quantify the goodness of freezing. We find that thefreezing index can be used to detect quantum phase transitions and discuss thecorresponding scaling behavior.
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