Three-dimensional Heisenberg spin glass under a weak random anisotropy

We perform a finite-size scaling study of the three-dimensional Heisenberg spin glass in the presence of weak random anisotropic interactions, up to lattice sizes $L=32$. Anisotropies have a major impact on the phase transition. The chiral-glass susceptibility does not diverge due to a large anomalous dimension. It follows that the anisotropic spin glass belongs to a Universality Class different from the isotropic model, which questions the applicability of the chirality scenario.

Figure 1

(Color online) Sample-averaged $$ defined in the left-hand side of Eq. (5) vs Monte Carlo time, as computed for $L=32$ at $T=0.187$ and $D=0.05$. The EMCS was defined in the caption of Table . Each point is an average over 3000 consecutive measurements.

Figure 2

(Color online) Correlation length in units of the lattice size vs $T$ for all our system sizes at $D=0.05$. Results for both the CG ( top), and the SG sectors ( bottom). Data patches correspond each to an independent simulation (we used data reweighting[32]). Inset: CG intersections for pairs of sizes $(L,2L)$. The range of $T$ and ${\xi }_{\mathit{CG}}/L$ differ from the main plot.

Figure 3

(Color online) Chiral-glass susceptibility ${\chi }_{\mathit{CG}}$ (top) and $I_1$ integral defined in Eq. (7) (bottom) vs temperature for all our system sizes with $D=0.05$. Lines are guides to eyes. Inset: zoom of ${\xi }_{\mathit{CG}}/L$ vs T.

Figure 4

(Color online) For all our lattice sizes at $D=0.1$, we show the chiral-glass susceptibility (top), as well as the CG (center) and SG (bottom) correlation lengths in units of the system size, as a function of temperature.