Monte Carlo studies of the ordering of the one-dimensional Heisenberg spin glass with long-range power-law interactions

Abstract

The nature of the ordering of the one-dimensional Heisenberg spin-glass model with a long-range power-law interaction is studied by extensive Monte Carlo simulations, with particular attention to the issue of the spin-chirality decoupling/coupling. Large system sizes up to $L=4096$ are studied. With varying the exponent $\sigma$ describing the power-law interaction, we observe three distinct types of ordering regimes. For smaller $\sigma$, the spin and the chirality order at a common finite temperature with a common correlation-length exponent, exhibiting the standard spin-chirality coupling behavior. For intermediate $\sigma$, the chirality orders at a temperature higher than the spin, exhibiting the spin-chirality decoupling behavior. For larger $\sigma$, both the spin and the chirality order at zero temperature. We construct a phase diagram in the $\sigma$ versus the temperature plane, and discuss implications of the results. Critical properties associated with both the chiral-glass and the spin-glass transitions are also determined.

arXiv comment28 pages, 26 figures, to appear in J. Phys. Soc. Jpn

References in corpus (18)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Diluted one-dimensional spin glasses with power law decaying interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Probing the Almeida-Thouless line away from the mean-field model
• Chiral-glass transition and replica symmetry breaking of a three-dimensional Heisenberg spin glass
• Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis
• The spin glass transition of the three dimensional Heisenberg spin glass
• Large-scale Monte Carlo simulations of the isotropic three-dimensional Heisenberg spin glass
• Chirality scenario of the spin-glass ordering
• Numerical evidence of the spin-chirality decoupling in the three-dimensional Heisenberg spin glass
• Nature of the phase transition of the three-dimensional isotropic Heisenberg spin glass
• Critical behaviour and ultrametricity of Ising spin-glass with long-range interactions
• Critical structure factor in Ising systems
• Spin-chirality decoupling in Heisenberg spin glasses and related systems
• Ordering of the Heisenberg Spin Glass in High Dimensions
• Zero-temperature phase of the XY spin glass in two dimensions: Genetic embedded matching heuristic
• Ordering of the Heisenberg spin glass in two dimensions
• Spin-chirality decoupling in the one-dimensional Heisenberg spin glass with long-range power-law interactions

Cited by in corpus (3)

• 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
• Ordering of the Heisenberg spin glass in four dimensions