  The existence of definite orders in frustrated quantum systems is related
rigorously to the occurrence of fully factorized ground states below a
threshold value of the frustration. Ground-state separability thus provides a
natural measure of frustration: strongly frustrated systems are those that
cannot accommodate for classical-like solutions. The exact form of the
factorized ground states and the critical frustration are determined for
various classes of nonexactly solvable spin models with different spatial
ranges of the interactions. For weak frustration, the existence of
disentangling transitions determines the range of applicability of mean-field
descriptions in biological and physical problems such as stochastic gene
expression and the stability of long-period modulated structures.
