Lattice distortion in disordered antiferromagnetic XY models

The behavior of lattice distortion in the spin 1/2 antiferromagnetic XY models with random magnetic modulation is investigated with the consideration of spin--phonon coupling in the adiabatic limit. It is found that the lattice distortion relies on the strength of the random modulation. For strong or weak enough spin--phonon couplings, the average lattice distortion may decrease or increase as the random modulation is strengthened. This may be the results of the competition between the random magnetic modulation and the spin--phonon coupling.