Three-dimensional Heisenberg Spin Glass Research Articles

Monte Carlo studies of the spin-chirality decoupling in the three-dimensional Heisenberg spin glass

An extensive equilibrium Monte Carlo simulation is performed on the 3D isotropic Heisenberg SG model with the random nearest-neighbor Gaussian coupling, with particular interest in its chiral-glass (CG) and spin-glass (SG) orderings. For this model, the possibility of the spin-chirality decoupling, {\it i.e.\}, the CG order setting in at a higher temperature than that of the SG order was suggested earlier, but still remains controversial. We simulate the model up to the maximum size (linear dimension) $L=48$ under both periodic and open boundary conditions (BC). In locating the CG and SG transition temperatures $T_{{\rm CG}}$ and $T_{{\rm SG}}$ by the $L\rightarrow \infty$ extrapolation, a variety of independent physical quantities under the both BC are computed and utilized to get larger number of degrees of freedom (NDF). Thanks to the large NDF up to NDF=43, we succeed in obtaining stable and accurate estimates of the CG and SG transition temperatures, $T_{{\rm CG}}=0.142\pm 0.001$ and $T_{{\rm SG}}=0.131^{+0.001}_{-0.006}$. No sign of the size crossover is observed. For larger $L$, the CG correlation length progressively outgrows the SG correlation length at low temperatures. These results provide strong numerical support for the spin-chirality decoupling. The critical exponents associated with the CG and SG transitions are evaluated by use of the finite-size scaling with the scaling correction. For the CG transition, we get the CG exponents, $\nu_{{\rm CG}}=1.36\pm 0.10$ and $\eta_{{\rm CG}}=0.49\pm 0.10$, consistently with the corresponding experimental exponents of canonical SG. Implications to the chirality scenario of experimental SG ordering is discussed.

Coexistence of the Kondo effect and spin glass physics in Fe-doped NbS2

We report the coexistence of the Kondo effect and spin glass behavior in Fe-doped NbS2 single crystals. The FexNbS2 shows the resistance minimum and negative magnetoresistance due to the Kondo effect, and exhibits no superconducting behavior at low temperatures. The resistance curve follows a numerical renormalization-group theory using the Kondo temperature K for x = 0.01 as evidence of Kondo effect. Scanning tunneling microscope/spectroscopy (STM/STS) revealed the presence of Fe atoms near sulfur atoms and asymmetric spectra. The magnetic susceptibility exhibits a feature of spin glass. The static critical exponents determined by the universal scaling of the nonlinear part of the susceptibility suggest a three-dimensional Heisenberg spin glass. The doped-Fe atoms in the intra- and inter-layers revealed by the x-ray result can realize the coexistence of the Kondo effect and spin glass.

Precursors of the spin glass transition in three dimensions

We study energy landscape and dynamics of the three-dimensional Heisenberg spin glass model in the paramagnetic phase, i.e. for temperature T larger than the critical temperature . The landscape is non-trivially related to the equilibrium states even in the high-temperature phase, and reveals an onset of non-trivial behavior at a temperature , which is also seen through the behavior of the thermoremanent magnetization. We also find a power-law growth of the relaxation times far from the spin-glass transition, indicating a dynamical crossover at a temperature , . The arising picture is reminiscent of the phenomenology of supercooled liquids, and poses questions on which mean-field models can describe qualitatively well the phenomenology in three dimensions. On the technical side, local energy minima are found with the Successive Overrelaxation algorithm, which reveals very efficient for energy minimization in this kind of models.

Soft Modes, Localization, and Two-Level Systems in Spin Glasses.

In the three-dimensional Heisenberg spin glass in a random field, we study the properties of the inherent structures that are obtained by an instantaneous cooling from infinite temperature. For a not too large field the density of states g(ω) develops localized soft plastic modes and reaches zero as ω(4) (for large fields a gap appears). When we perturb the system adding a force along the softest mode, one reaches very similar minima of the energy, separated by small barriers, that appear to be good candidates for classical two-level systems.

Phase transition in three-dimensional Heisenberg spin glasses with strong random anisotropies through a multi-GPU parallelization

We characterize the phase diagram of anisotropic Heisenberg spin glasses, finding both the spin and the chiral glass transition. We remark the presence of strong finite-size effects on the chiral sector. We find a unique phase transition for the chiral and spin glass sector, in the Universality class of Ising spin glasses. We focus on keeping finite-size effects under control, and we stress that they are important to understand experiments. Thanks to large GPU clusters we have been able to thermalize cubic lattices with up to 64x64x64 spins, over a vast range of temperatures.

Critical exponents and irreversibility lines of La0.9Sr0.1CoO3 single crystal

We have studied the dynamic and static critical behavior of spin glass transition in insulating La0.9Sr0.1CoO3 single crystal by ac susceptibility and dc magnetization measurements in the vicinity of its freezing temperature (Tf). The dynamic scaling analysis of the frequency dependence of ac susceptibility data yields the characteristic time constant τ0=1.6(9)×10−12 s, the dynamic critical exponent zν=9.5(2), and a frequency dependence factor K=ΔTf/Tf(Δlogf)=0.017, indicating that the sample enters into a canonical spin-glass phase below Tf = 34.8(2) K. The scaling analysis of non-linear magnetization in the vicinity of Tf through the static scaling hypothesis yields critical exponents β = 0.89(1) and γ = 2.9(1), which match well with that observed for well known three-dimensional (3D) Heisenberg spin glasses. From the longitudinal component of zero-field-cooled and field-cooled magnetization measurement, we have constructed the H–T phase diagram which represents the field evolution of two characteristic temperatures: the upper one, Tw(H), indicates the onset of spin freezing in a uniform external field H, while the lower one, Ts(H), marks the onset of strong irreversibility of the frozen state. The low field Ts(H) follows the critical line suggested by d'Almeida-Thouless model for canonical spin glass, whereas the Tw(H) exhibits a re-entrant behavior with a maximum in the Tw(H) at a nonzero field above which it follows the Gabay-Toulouse (GT) critical line which is a characteristic of Heisenberg spin glass. The reentrant behavior of the GT line resembles that predicted theoretically for n-component vector spin glasses in the presence of a uniaxial anisotropy field.

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 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.

Speeding up parallel tempering simulations

We discuss methods that allow us to increase the step size in a parallel tempering simulation of statistical models and test them at the example of the three-dimensional Heisenberg spin glass. We find an overall speedup of about 2 for contemporary lattices.

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

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, ${T}_{CG}>{T}_{SG}>0$. Hence, the spin and the chirality are decoupled in the ordering of the model. The chiral-glass exponents are estimated to be ${\ensuremath{\nu}}_{CG}=1.4\ifmmode\pm\else\textpm\fi{}0.2$ and ${\ensuremath{\eta}}_{CG}=0.6\ifmmode\pm\else\textpm\fi{}0.2$, 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.

Numerical Evidence of Spin-Chirality Decoupling in the Three-Dimensional Heisenberg Spin Glass Model

Ordering of the three-dimensional Heisenberg spin glass with Gaussian coupling is studied by extensive Monte Carlo simulations. The model undergoes successive chiral-glass and spin-glass transitions at nonzero temperatures T_{CG}>T_{SG}>0, exhibiting spin-chirality decoupling.

Large-scale Monte Carlo simulations of the isotropic three-dimensional Heisenberg spin glass

We study the Heisenberg spin glass by large-scale Monte Carlo simulations for sizes up to 32^3, down to temperatures below the transition temperature claimed in earlier work. The data for the larger sizes show more marginal behavior than that for the smaller sizes, indicating the lower critical dimension is close to, and possibly equal to three. We find that the spins and chiralities behave in a quite similar manner.

Comment on “Spin-Glass Transition of the Three-Dimensional Heisenberg Spin Glass”

Campos et al. [Phys. Rev. Lett. 97 (2006) 217204] claim that in the 3d Heisenberg Spin Glass, chiral and spin sector ordering temperatures are identical. We point out that in their analysis of their numerical data key assumptions are made which are unjustified.

Finite temperature phase transition in the three-dimensional Heisenberg ±J spin glass model

The three-dimensional Heisenberg spin glass model with ±J interactions is studied using an over-relaxed Monte Carlo algorithm. We have measured the correlation length ξ, and using the crossing of ξ∕L for different L find a finite temperature spin glass transition, with TSG=0.220(5). In addition, we have varied the number of Monte Carlo steps used prior to, and during, thermal averaging to control the effects of finite time averaging. We find that the over-relaxation algorithm allows for an accurate measurements using as few as 300 Monte Carlo steps.

Spin–chirality decoupling in Heisenberg spin glasses and related systems

Recent studies on the spin and the chirality orderings of the three-dimensional Heisenberg spin glass (SG) and related systems are reviewed with particular emphasis on the possible spin–chirality decoupling phenomena. Chirality scenario of real SG transition and its experimental consequence on the ordering of Heisenberg-like SGs are discussed.

Monte Carlo simulations of the phase transition of the three-dimensional isotropic Heisenberg spin glass

Equilibrium properties of the three-dimensional isotropic Heisenberg spin glass are studied by extensive Monte Carlo simulations, with particular attention paid to the nature of its phase transition. A finite-size-scaling analysis is performed for both the spin-glass (SG) and chiral-glass (CG) orders. Our results suggest that the model exhibits the CG long-range order at finite temperatures without accompanying the conventional SG long-range order, in contrast to some of the recent works claiming a simultaneous SG and CG transition. Typical length and time scales which represent a crossover from the spin-chirality coupling regime at short scales to the spin-chirality decoupling regime at long scales are introduced and examined in order to observe the true asymptotic transition behavior. On the basis of these crossover scales, discussion is given concerning the cause of the discrepancy between our present result and those of other recent numerical works.

Nature of the Ordering of Three-Dimensional Heisenberg Spin Glasses

Spin-glass and chiral-glass orderings of the three-dimensional Heisenberg spin glass are studied by large-scale equilibrium Monte Carlo simulations. A finite-size scaling analysis of the squared order parameters both for spin and chirality shows that a freezing temperature of the spin-glass order is lower than that of the chiral-glass one, namely there exists a chiral-glass phase in which the chirality exhibits a long range order without a conventional spin glass order. Our results support a spin-chirality decoupling picture, which is a basic assumption of a chirality scenario of experimentally observed spin-glass transition.

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

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.

Fluctuation?dissipation ratio of the Heisenberg spin glass

Fluctuation–dissipation relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation.

Time and length scales in spin glasses

We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy phase. Webriefly review the present theoretical understanding of the spectacular phenomena observedin experiments and describe new numerical results obtained in the first large-scalesimulation of the nonequilibrium dynamics of the three-dimensional Heisenberg spinglass.

Replica symmetry breaking transition of the weakly anisotropic Heisenberg spin glass in magnetic fields.

The spin and the chirality orderings of the three-dimensional Heisenberg spin glass with the weak random anisotropy are studied under applied magnetic fields by equilibrium Monte Carlo simulations. A replica symmetry breaking transition occurs in the chiral sector accompanied by the simultaneous spin-glass order. The ordering behavior differs significantly from that of the Ising spin glass, despite the similarity in the global symmetry. Our observation is consistent with the spin-chirality decoupling-recoupling scenario of a spin-glass transition.