Ordering of the Heisenberg spin glass in two dimensions

Abstract

The spin and the chirality orderings of the Heisenberg spin glass in two dimensions with the nearest-neighbor Gaussian coupling are investigated by equilibrium Monte Carlo simulations. Particular attention is paid to the behavior of the spin and the chirality correlation lengths. In order to observe the true asymptotic behavior, fairly large system size L\gsim 20 (L the linear dimension of the system) appears to be necessary. It is found that both the spin and the chirality order only at zero temperature. At high temperatures, the chiral correlation length stays shorter than spin correlation length, whereas at lower temperatures below the crossover temperature T_\times, the chiral correlation length exceeds the spin correlation length. The spin and the chirality correlation-length exponents are estimated above T_\times to be ν_SG=0.9+-0.2 and ν_CG=2.1+-0.3, respectively. These values are close to the previous estimates on the basis of the domain-wall-energy calculation. Discussion is given about the asymptotic critical behavior realized below T_\times.

arXiv commentto appear in a special issue of J. Phys. A

References in corpus (10)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Chiral-glass transition and replica symmetry breaking of a three-dimensional Heisenberg spin glass
• Dynamical simulation of spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses
• Spin-Glass and Chiral-Glass Transitions in a $\pm J$ Heisenberg Spin-Glass Model in Three Dimensions
• A common Universality class for the three-dimensional Vortex Glass and Chiral Glass?
• Stiffness of the Heisenberg Spin-Glass Model at Zero- and Finite-Temperatures in Three Dimensions
• Ordering of the three-dimensional Heisenberg spin glass in magnetic fields
• Monte Carlo Studies of the Ordering of the Three-Dimensional Isotropic Heisenberg Spin Glass in Magnetic Fields
• Study of Chirality in the Two-Dimensional XY Spin Glass
• Ordering of the Heisenberg Spin Glass in High Dimensions

Cited by in corpus (10)

• Chirality scenario of the spin-glass ordering
• Nature of the phase transition of the three-dimensional isotropic Heisenberg spin glass
• Flux $1/f^{\alpha }$ noise in 2D Heisenberg spin glasses: effects of weak anisotropic interactions
• Monte Carlo studies of the spin-chirality decoupling in the three-dimensional Heisenberg spin glass
• Monte Carlo simulations of the three-dimensional XY spin glass focusing on the chiral and the spin order
• Spin-chirality decoupling in the one-dimensional Heisenberg spin glass with long-range power-law interactions
• Ordering of the Heisenberg spin glass in four dimensions
• Spin and chirality orderings of the one-dimensional Heisenberg spin glass with the long-range power-law interaction
• Monte Carlo studies of the ordering of the one-dimensional Heisenberg spin glass with long-range power-law interactions
• Multiscaling in the YX model of networks