We study the effects of quenched bond disorder in frustrated easy-plane antiferromagnets in two space dimensions, using a combination of analytical and numerical techniques. We consider local-moment systems which display noncollinear long-range order at zero temperature, with the antiferromagnetic triangular-lattice $XY$ model as a prime example. We show that (i) weak bond disorder transforms the clean ground state into a state with quasi-long-range order, and (ii) strong bond disorder results in a short-range-ordered glassy ground state. Using extensive Monte Carlo simulations, we also track the fate of the quasi-long-range-ordered phase at finite temperature and the associated Kosterlitz-Thouless-like transition. Making contact with previous studies of disordered $XY$ models, we discuss similarities and differences concerning the interplay of disorder and frustration. Our results are also of relevance to noncollinear Heisenberg magnets in an external magnetic field.

• Received 14 May 2020
• Revised 21 July 2020
• Accepted 2 September 2020

DOI:https://doi.org/10.1103/PhysRevB.102.125121