Ordering of the Heisenberg spin glass in two dimensions

TL;DR

This study uses Monte Carlo simulations to investigate the ordering behavior of the two-dimensional Heisenberg spin glass, revealing that both spin and chirality order only at zero temperature and analyzing their correlation lengths and critical exponents.

Contribution

It provides the first detailed analysis of the zero-temperature ordering and correlation-length exponents of the 2D Heisenberg spin glass, emphasizing the importance of large system sizes.

Findings

Both spin and chirality order only at zero temperature.

Chiral correlation length exceeds spin correlation length below crossover temperature.

Estimated correlation-length exponents: ν_SG=0.9±0.2, ν_CG=2.1±0.3.

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 \nu_SG=0.9+-0.2 and \nu_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.