Chiral order in a two-dimensionalXYspin glass

Ordering phenomena in the two-dimensional $\mathrm{XY}$ (plane-rotator) spin glass are studied by Monte Carlo simulations, with particular attention to the behavior of the chirality, which is an Ising-like multispin variable associated with a broken reflection symmetry. The chiral degrees of freedom are found to order in a markedly different manner from the $\mathrm{XY}$ spins: Indeed, the chiral susceptibility can be accurately mapped onto the spin-glass susceptibility of a pure Ising spin glass.