Chirality-glass and spin-glass correlations in the two-dimensional random-bondXYmodel

The nearest-neighbor XY spin-glass model on square lattices with both Gaussian and random ±{}J bond distributions has been studied by Monte Carlo simulations and the results analyzed by finite-size scaling methods. For both bond distributions, we find a power-law divergence of the spin-glass correlation length, {ξ}{~}T^-ν, as T{→}0, with {ν}{}1. The exponent {η}, which describes the decay of correlations at zero temperature, is {}0 for the Gaussian bond distribution, but for ±{}J bonds, {η} attains a small positive value {~}0.15, implying that the ground state is highly degenerate. The chiral degrees of freedom also exhibit glass ordering as T{→}0, with the chiralities ordered randomly without any spatial periodicity. The correlation-length exponent νc corresponding to the chiral glass ordering as T{→}0 is {}2 for both kinds of bond distribution. The different values obtained for {ν} and νc suggest that there may be two distinct correlation lengths associated with this zero-temperature phase transition.