Weakening of antiferromagnetism due to frustration on inhomogeneous 2D lattices

I consider the ground state of quantum spins interacting via Heisenberg antiferromagnetic exchange, in lattices having several types of local environment. In unfrustrated cases, when a Néel type order exists, it is known that quantum fluctuations are site-dependent, and lead to an inhomogeneous local staggered order parameter. This paper discusses some effects of adding frustration to such a system, by including next nearest neighbor antiferromagnetic interactions. Within linear spinwave theory, it is found that as the frustration parameter increases, the local order parameters decrease at a rate that depends on the type of sites involved in the frustrated loops. The cases of a decorated square lattice system, and of a quasiperiodic tiling are considered to study difierent ways in which antiferromagnetism is suppressed in these inhomogeneous systems.