Monte Carlo studies of chiral and spin ordering of the three-dimensional Heisenberg spin glass

Abstract

The nature of the ordering of the three-dimensional isotropic Heisenberg spin glass with nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. Several independent physical quantities are measured both for the spin and for the chirality, including the correlation-length ratio, the Binder ratio, the glass order parameter, the overlap distribution function, and the nonself-averageness parameter. By controlling the effect of the correction-to-scaling, we have obtained a numerical evidence for the occurrence of successive chiral-glass and spin-glass transitions at nonzero temperatures, T CG Ͼ T SG Ͼ 0. Hence, the spin and the chirality are decoupled in the ordering of the model. The chiral-glass exponents are estimated to be CG = 1.4Ϯ 0.2 and CG = 0.6Ϯ 0.2, indicating that the chiral-glass transition lies in a universality class different from that of the Ising spin glass. The possibility that the spin and chiral sectors undergo a simultaneous Kosterlitz-Thouless-type transition is ruled out. The chiral-glass state turns out to be nonself-averaging, possibly accompanying a one-step-like peculiar replica-symmetry breaking. Implications to the chirality scenario of experimental spin-glass transitions are discussed.

Ordering of the Heisenberg spin glass in four dimensions

“…As mentioned above, the negative dip of g CG shown in Fig.3(b) is consistent with the occurrence of a one-steplike RSB [16,18,19]. The corresponding spin Binder ratio g SG shown in Fig.3(b) also develops a more and more singular form with a peak structure appearing for larger L. If one recalls the fact that g SG takes a value unity at T = 0 and approaches zero above T SG (= T CG ) in the L → ∞ limit, g SG is expected to develop a negative dip as in the case of g CG .…”

“…In fact, such a form of g is expected in a system with an ordered state exhibiting a continuous one-step-like replica-symmetry breaking (RSB) [33]. A similar form of g CG was observed in 3D [16,18,19]. Note that the one-step-like RSB discussed here is of a continuous type, in contrast to the one-step RSB of a discontinuous type often discussed in conjunction with structural glasses.…”

“…A possible counter-view to such a picture might be that the spin and the chirality order at a common finite temperature [10][11][12][13][14]. Although there is no complete consensus, recent simulations point to the occurrence of the spin-chirality decoupling in 3D [15][16][17][18][19]. For example, Ref.…”

Critical phenomena of canonical spin glass systems with large Dzyaloshinsky–Moriya anisotropy

“…Therefore, we conclude that the values of the critical exponents are different from those of AuFe in [14] and that the universality class of PtMn belongs to the same universality class of the other canonical systems. These values well coincide with those of the chirality theory [13]. However, the direct observation of the critical phenomena in chiral susceptibilities, anomalous Hall effect [8,16], is necessary for the final conclusion.…”

From measurements to inferences of physical quantities in numerical simulations

“…One of the most important and unsolved problems in spin-glass studies is the coupling or separation of the spin-glass (sg) degrees of freedom and chiral-glass (cg) degrees of freedom [18,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Kawamura [25,26] introduced the chirality scenario, wherein the cg order exists without the sg order.…”