Monte Carlo study of the ordering of the weakly anisotropic Heisenberg spin glass in magnetic fields

Abstract

The ordering of the three-dimensional Heisenberg spin glass with the weak random anisotropy in magnetic fields is studied by extensive equilibrium Monte Carlo simulations. Both the spin and the chirality are monitored. We find strong numerical evidence that a replica symmetry breaking transition occurs in the chiral sector, which accompanies the simultaneous spin-glass order. Despite the similarity in the global symmetry, the ordering behavior of the weakly anisotropic Heisenberg spin glass differs significantly from that of the strongly anisotropic Ising spin glass. The obtained phase diagram in the temperature -magnetic field plane is similar to the experimental phase diagram. Our results highlight the importance of the chirality in the spin-glass ordering of the Heisenberg-like spin glass, and support the spin-chirality decoupling-recoupling scenario of spin-glass transitions.

Heisenberg Spin Glass Experiments and the Chiral Ordering Scenario

“…However successive interpretations of the numerical data are not always consistent with each other, and further analysis together with improved numerical work have shown some of these interpretations to be flawed 15,25) . Direct 3d numerical results 15,16,17,18,19) reinforced by indirect arguments from 1d simulations 20) provide evidence strongly in favor of the chiral driven ordering scenario for a pure short range spin-spin interaction 3d EA Heisenberg model. To summarize the conclusions drawn in Ref.…”

“…This difference suggests a chiral mechanism in the Heisenberg case. Kawamura and collaborators 16,17,18,19) have underlined the fact that in the simulations the chiral Binder parameter data, which go through a strong negative dip above T c , should be interpreted in terms of a 1-step RSB transition. This corresponds to states below the transition temperature which are essentially orthogonal to each other.…”

“…A negative dip of the chiral Binder cumulant at temperatures above T CG indicates that the chiral ordering has a 1-step RSB character. The chiral phase transition persists under very strong applied fields 18) as the coupling between the field and the chiral glass order parameter is much weaker than between the field and the spin glass order parameter. This model is presented fully in a companion article by H. Kawamura 26) .…”

“…The phase transition for a model Heisenberg spin glass in which a weak anisotropy term was introduced was shown in Ref. 18) . The experimental and model behaviors are strikingly similar, including the temperature of the vertical line which is slightly lower than T c in both cases.…”

“…See Table I for the DM anisotropies. Inset : model H(T ) phase line for HSG with anisotropy D = 0.05 18 ) used are typically ∼ 10 4 seconds). The temperature is then increased back to T 1 and is held there for a further time t 3 .…”