Monte Carlo studies of chiral and spin ordering of the three-dimensional Heisenberg spin glass

Abstract

The nature of the ordering of the three-dimensional isotropic Heisenberg spin glass with nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. Several independent physical quantities are measured both for the spin and for the chirality, including the correlation-length ratio, the Binder ratio, the glass order parameter, the overlap distribution function, and the nonself-averageness parameter. By controlling the effect of the correction-to-scaling, we have obtained a numerical evidence for the occurrence of successive chiral-glass and spin-glass transitions at nonzero temperatures, ${T}_{CG}>{T}_{SG}>0$. Hence, the spin and the chirality are decoupled in the ordering of the model. The chiral-glass exponents are estimated to be ${\ensuremath{\nu}}_{CG}=1.4\ifmmode\pm\else\textpm\fi{}0.2$ and ${\ensuremath{\eta}}_{CG}=0.6\ifmmode\pm\else\textpm\fi{}0.2$, indicating that the chiral-glass transition lies in a universality class different from that of the Ising spin glass. The possibility that the spin and chiral sectors undergo a simultaneous Kosterlitz-Thouless-type transition is ruled out. The chiral-glass state turns out to be nonself-averaging, possibly accompanying a one-step-like peculiar replica-symmetry breaking. Implications to the chirality scenario of experimental spin-glass transitions are discussed.