Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis

We have investigated the phase transition in the Heisenberg spin glass using massive numerical simulations to study very large sizes, ${48}^3$. A finite-size scaling analysis indicates that the data are compatible with the most economical scenario: a common transition temperature for spins and chiralities.

Figure 1

(Color online) Top: parallel tempering autocorrelation function (Ref. 23), as computed for three representative $L=48$ samples. Here easy means that after $N_{\text{sweep}}^{\text{min}}$ MC steps, see Table , the equilibration criterion was met (42% of samples), while medium samples (34%) required up to $2N_{\text{sweep}}^{\text{min}}$ MC steps. Bottom: the quantity $\Delta$ in Eq. (12) as a function of MC time, both in units of $N_{\text{sweep}}^{\text{min}}$ (red triangles) and in units of the maximum number of sweeps for each sample (blue circles). For the latter, note that the data are computed at different times for different samples.

Figure 2

(Color online) Data for the spin-glass and chiral-glass correlation lengths divided by system size. For $L\to \infty$ the data should intersect at the transition temperature. Here, the data do not show a common intersection temperature indicating that there are strong corrections to scaling for the range of sizes studied.

Figure 3

(Color online) Data for the spin-glass and chiral-glass Binder ratios defined in Eq. (5) of the text.