Order by geometrical disorder in a 2D quantum antiferromagnet

We consider the effects of random fluctuations in the local geometry on the ground state properties of a two-dimensional quantum antiferromagnet. We analyse the behavior of spins described by the Heisenberg model as a function of what we call ``phason flip disorder,'' following a terminology used for aperiodic systems. The calculations were carried out both within linear spin wave theory and using quantum Monte Carlo simulations. An ``order by disorder'' phenomenon is observed in this model, wherein antiferromagnetism is found to be enhanced by phason disorder. The value of the staggered order parameter increases with the number of defects, accompanied by an increase in the ground state energy of the system. We furthermore find a long-ranged attractive Casimir-like force between two domain walls of defects separated by a finite distance.