  Ginzburg-Landau theory of continuous phase transitions implicitly assumes
that microscopic changes are negligible in determining the thermodynamic
properties of the system. In this work we provide an example that clearly
contrasts with this assumption. We show that topological frustration can change
the nature of a second order quantum phase transition separating two different
ordered phases. Even more remarkably, frustration is triggered simply by a
suitable choice of boundary conditions in a 1D chain. While with every other BC
each of two phases is characterized by its own local order parameter, with
frustration no local order can survive. We construct string order parameters to
distinguish the two phases, but, having proved that topological frustration is
capable of altering the nature of a system's phase transition, our results pose
a clear challenge to the current understanding of phase transitions in complex
quantum systems.
