Monte Carlo simulations of the three-dimensionalXYspin glass focusing on chiral and spin order

Abstract

The ordering of the three-dimensional isotropic XY spin glass with the nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. To investigate the ordering of the spin and the chirality, we compute several independent physical quantities including the glass order parameter, the Binder parameter, the correlation-length ratio, the overlap distribution and the non-self-averageness parameter, etc, for both the spin-glass (SG) and the chiral-glass (CG) degrees of freedom. Evidence of the spin-chirality decoupling, i.e., the CG and the SG order occurring at two separated temperatures, 0 < TSG < TCG, is obtained from the glass order parameter, which is fully corroborated by the Binder parameter. By contrast, the CG correlation-length ratio yields a rather pathological and inconsistent result in the range of sizes we studied, which may originate from the finite-size effect associated with a significant short-length drop-off of the spatial CG correlations. Finite-size-scaling analysis yields the CG exponents νCG = 1.36 +0.15 −0.37 and ηCG = 0.26 +0.29 −0.26 , and the SG exponents νSG = 1.22 +0.26 −0.06 and ηSG = −0.54 +0.24 −0.52 . The obtained exponents are close to those of the Heisenberg SG, but are largely different from those of the Ising SG. The chiral overlap distribution and the chiral Binder parameter exhibit the feature of a continuous one-step replicasymmetry breaking (1RSB), consistently with the previous reports. Such a 1RSB feature is again in common with that of the Heisenberg SG, but is different from the Ising one, which may be the cause of the difference in the CG critical properties from the Ising SG ones despite of a common Z2 symmetry.

Non-self-averaging in Ising spin glasses and hyperuniversality

“…In the light of the nonself-averaging behavior reported above for the ISG models, it is clear that the published spin and chiral nonself-averaging data [29][30][31] in 3D Heisenberg and XY models are incompatible with a spin-driven ordering scenario [23][24][25][26][27] but strongly support the alternative conclusion that the spin glass ordering in these models is chiral-driven rather than spin-driven, on the Kawamura scenario [28]. An important implication is that order in the canonical experimental Heisenberg spin glasses is also chirality driven.…”

“…According to the first interpretation, the ordering is spin-spin interaction driven; basically the ordering process is much the same as in ISGs, and the chiral order follows on as a geometrically necessary consequence of the onset of spin order, without the chiral interactions playing any significant role in the spin glass transition [23][24][25][26][27]. The alternative interpretation is that the driving role in 3D HSG or XYSG ordering is played by the chirality, so that there is first a chiral order onset followed at a lower temperature by spin ordering transition [28][29][30][31]. (Similar disagreements concerning fully frustrated 2D XY models were resolved definitively in favor of a distinct chiral order transition just above a spin order transition [32,33]).…”

“…-there is a strong U 22c (T, L) peak at an almost Lindependent temperature T ≈ 0.19, T ≈ 0.145, T ≈ 0.31 respectively, so in each case close to the T c (c) value estimated independently from other criteria [29][30][31]. In the paramagnetic regime there is a regular narrowing in temperature of the U 22c (T, L) peak with increasing L which appears compatible with the Aharony-Harris law U 22c (T, L) ∼ (ξ c (T, L)/L) 3 though the data are not presented in this form.…”

“…No non-self-averaging results were reported. From detailed 3D bimodal and Gaussian HSG and 3D Gaussian XYSG measurements, the two separate transition temperatures on the chiral-driven ordering scenario are estimated to be (bimodal HSG) [29], T c (c) = 0.194(5) and T c (s) ≤ 0.15, (Gaussian HSG) T c (c) = 0.143(3) and T c (s) = 0.125(+0.006/ − 0.012) [30], and (XYSG) T c (c) = 0.308(5) and T c (s) = 0.274(3) [31]. Non-self-averaging data were shown in each case.…”

Event-chain Monte Carlo for classical continuous spin models

“…Particularly frustrating is the case of the threedimensional XY spin glass model, where the algorithm loses all its power [11,12]. For this much studied spin glass model, our understanding today resembles the one of the XY model before the revolution triggered by the cluster algorithms.…”