Chirality-glass and spin-glass correlations in the two-dimensional random-bond XY model.

Abstract

The nearest-neighbor XY spin-glass model on square lattices with both Gaussian and random \ifmmode\pm\else\textpm\fi{}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, \ensuremath{\xi}\ensuremath{\sim}${\mathit{T}}^{\mathrm{\ensuremath{-}}\ensuremath{\nu}}$, as T\ensuremath{\rightarrow}0, with \ensuremath{\nu}\ensuremath{\simeq}1. The exponent \ensuremath{\eta}, which describes the decay of correlations at zero temperature, is \ensuremath{\simeq}0 for the Gaussian bond distribution, but for \ifmmode\pm\else\textpm\fi{}J bonds, \ensuremath{\eta} attains a small positive value \ensuremath{\sim}0.15, implying that the ground state is highly degenerate. The chiral degrees of freedom also exhibit glass ordering as T\ensuremath{\rightarrow}0, with the chiralities ordered randomly without any spatial periodicity. The correlation-length exponent ${\ensuremath{\nu}}_{\mathit{c}}$ corresponding to the chiral glass ordering as T\ensuremath{\rightarrow}0 is \ensuremath{\simeq}2 for both kinds of bond distribution. The different values obtained for \ensuremath{\nu} and ${\ensuremath{\nu}}_{\mathit{c}}$ suggest that there may be two distinct correlation lengths associated with this zero-temperature phase transition.