  A general formalism of the relation between geometric phases produced by
circularly evolving interacting spin systems and their criticality behavior is
presented. This opens up the way for the use of geometric phases as a tool to
study regions of criticality without having to undergo a quantum phase
transition. As a concrete example a spin-1/2 chain with XY interactions is
presented and the corresponding geometric phases are analyzed. The
generalization of these results to the case of an arbitrary spin system
provides an explanation for the existence of such a relation.
