Short-range Spin Glasses Research Articles

Aging behaviour in two- and three-dimensional Ising spin glasses studied by Monte Carlo simulations

The nonequilibrium character of the spin glass dynamics has been studied in Monte Carlo simulations of two- and three-dimensional short-range Ising spin glass systems. The spin system was quenched in zero field to a temperature T. After equilibrating for a waiting time t w a weak magnetic field was applied and the time dependence of the magnetization M( t) was studied. Our results show that the relaxation rate, S( t) = ∂M( t)/ ∂log t, exhibits a maximum at a time t ≈ t w, which is consistent with results from experiments. If the temperature is increased or decreased prior to the field application, the apparent age t a of the system, as defined by the maximum in relaxation rate, is changed. The results are qualitatively in agreement with experiments as well as with theoretical models for the nonequilibrium spin glass dynamics.

Contours of constant χSG in the H-T plane: Mean-field versus droplet theories of Ising spin glasses

One of the central features of the mean-field theory of Ising spin glasses is the de Almeida-Thouless phase transition line in the H-T plane, where the spin-glass susceptibility χSG diverges. Contours of constant χSG in the paramagnetic phase go to high fields as T→0 in mean-field theory. In contrast, in the droplet theory for short-ranged spin glasses, χSG remains finite in a field and the contours go to H=0 as T→0. We have investigated the constant χSG contours both in the SK model and for d-dimensional short-ranged spin glasses. For the latter we use transfer matrix methods in d=1 and high-temperature expansions and Monte Carlo simulations in higher d. The results are in good accord with droplet theory for d=1 and 2. For d=3 the evidence remains ambiguous, although extrapolations of high-temperature series are qualitatively different from d=2.

Nonstationary dynamics in a two-dimensional spin glass

Aging is observed in the two-dimensional short-range Ising spin glass Rb2Cu0.78Co0.22F4 (Tc = 0 K) by means of low-frequency ac susceptibility and zero-field-cooled (ZFC) magnetization measurements. Below the freezing temperature (∼3.5 K), slow logarithmic relaxations are found in both the in-phase and out-of-phase ac susceptibility, and a waiting time dependence is observed in the relaxation of the zero-field-cooled magnetization. No saturation of the relaxations was found. The results suggest that the aging is governed by activated dynamics at length scales smaller than the equilibrium spin-glass correlation length.

Static scaling in a short-range Ising spin glass.

The nonlinear ac susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{nl}}^{\ensuremath{'}}$ of the short-range Ising spin glass ${\mathrm{Fe}}_{0.5}$${\mathrm{Mn}}_{0.5}$${\mathrm{TiO}}_{3}$ has been measured using a superconducting-quantum-interference-device magnetometer. The spin-glass temperature, ${\mathrm{T}}_{\mathrm{g}}$, and the critical exponent \ensuremath{\gamma} were estimated from the temperature dependence of the quadratic field term of ${\mathrm{\ensuremath{\chi}}}_{\mathrm{nl}}^{\ensuremath{'}}$, yielding ${\mathrm{T}}_{\mathrm{g}}$=20.70 and \ensuremath{\gamma}=4.0. Static-scaling analyses, using different scaling equations, gave similar results. Using \ensuremath{\gamma} and results from previous dynamic-scaling analyses, a number of critical exponents have been obtained through different scaling relations, e.g., \ensuremath{\delta}=8.4 and \ensuremath{\nu}=1.7. The results support the existence of a finite-temperature phase transition in a three-dimensional Ising spin glass.

Dynamical Simulation of the Heisenberg Spin Glass in Three Dimensions

An efficient method of simulating the Heisenberg model is proposed taking into account the spin dynamics, and applied to a short-range Heisenberg spin glass on a simple cubic lattice. Our method shows a drastic reduction in relaxation times and clearly reveals the vanishing of the order parameter q and the divergence of the susceptibility according to the Curie law as the temperature is decreased.

Monte carlo methods and glassy systems

Abstract The Monte Carlo method in statistical mechanics yields both equilibrium averages for model systems and information on relaxation processes described by master equations. It is a very useful tool for the study of short range spin glasses and orientational glasses. The numerical results for three—dimensional Ising and Potts glasses suggest an equilibrium phase transition to a glass phase at a nonzero freezing temperature, Tf>0. Freezing of isotropic spin and quadrupolar glasses is a nonequilibrium phenomenon, associated with a zero—temperature transition (Tf=0). All these systems are compatible with a Kohlrausch—type relaxation, i.e. the time—dependent Edwards—Anderson order parameter q(t) decays with time t as q(t)∼exp[—(t/τ)-y] for T>Tf. Since the relaxation time τ increases dramatically at low temperatures, it is very difficult to obtain accurate results on these models, and many open questions remain.

Long-time relaxation behavior in orientational glasses

The long-time relaxation observed in the orientational glass phase of solid ortho-parahydrogen mixtures is related to the low-temperature specific heat using a simple unified model. The use of stimulated spin echoes to study slow molecular motions is discussed in detail. The analysis is based on the domination of low-energy large-scale cluster excitations in the relaxation processes as introduced in Fisher and Huse's recent picture of the low-temperature behavior of short-range spin glasses.

Mean-field theory and fluctuations in Potts spin glasses. I

A short-range Potts spin glass is studied. A stable, non-marginal, mean-field theory is found with one level of replica symmetry breaking and a discontinuous transition for p>4. A complete stability analysis is provided, and two different correlation lengths are found above eight dimensions. The fluctuations in the ordered phase around this solution are incorporated in a renormalisation group approach and it is found that for a small range of the parameters they restore scaling close to the upper critical dimension. For the three-state case it appears that fluctuations destroy the stability of the solution for d<or=8 and cause the system to undergo a first-order phase transition. Non-universal corrections to the equation of state above the upper critical dimension are discussed.

Spectrum of the correlation matrix in short-range Ising spin glasses.

In the droplet picture of the scaling theory for the short-range Ising spin glass, the largest eigenvalue of the correlation matrix diverges algebraically with the Edwards-Anderson susceptibility, the exponent being d/(d-\ensuremath{\theta}), where \ensuremath{\theta} is the stiffness exponent. The spectral density for the correlation matrix has a bump near the lower edge of the spectrum. Comparing these predictions with results from numerical studies of the spectrum might provide a unique test of the droplet picture.

Equilibrium magnetic fluctuations of a short-range Ising spin glass.

Etude des fluctuations magnetiques d'equilibre de Fe 0.5 Mn 0.5 TiO 3 dans un magnetometre a support d'interferences quantique supraconducteur (SQID). Aux temperatures superieures a la temperature du verre de spins, le spectre de la puissance du bruit presente une dependance en 1/f aux hautes frequences, et une convergence vers des plateaux a la limite des basses frequences. En dessous de la temperature du verre de spins, on n'observe qu'une dependance en 1/f. Les fluctuations magnetiques et la composante out-of-phase de la susceptibilite-ac presentent un comportement en accord avec les predictions du theoreme de la dissipation de fluctuation. La forme fonctionnelle de la relaxation utilisee pour decrire les resultats des simulations Monte Carlo rend bien compte des comportements etudies

Phase transition in random-anisotropy magnets.

Results of computer simulations on random-anisotropy-axis model (RAM) are reported in the limit of infinite anisotropy. Finite-size scaling analyses of the data for equilibrium averages indicates a zero-temperature phase transition in two dimensions. The critical exponents are similar to those found for short-range Ising-spin-glass models in two dimensions. These results support the argument that RAM and short-range Ising spin-glass models belong to the same universality classes.

Low-frequency dynamics of orientational glasses.

We provide a unified explanation of the low-frequency relaxation and the low-temperature specific heat of the orientational-glass plase of solid ortho-para hydrogen mixtures. The analysis is based on Fisher and Huse's recent picture of the short-range spin glasses and the domination of the long-term relaxation by low-energy large-scale-cluster excitations.

Short-range Ising spin glasses in general dimensions

The equilibrium properties of nearest-neighbor Ising spin glasses on hypercubic lattices are studied as a function of d, the dimensionality. An expansion of Tc(d) to fifth order in inverse powers of d, augmented by high-temperature series estimates for d=3 and 4, yields the critical temperature for all d and for general, symmetric distributions of coupling strengths, Jij. By extrapolation of Tc to zero, the lower borderline dimensionality is estimated as dl ≂2.5. High-temperature expansions for the spin-glass susceptibility of the ±J model in powers of w=tanh2(J/kBT) and u=tanh2(H/kBT), where H is the magnetic field, yield estimates of the magnetic field crossover exponent Δ for d=3 to 8.

A Monte Carlo study of realistic models of metallic spin glasses

Monte Carlo simulation methods are used to study the critical behaviour of the classical Ruderman-Kittel-Kasuya-Yosida model (RKKY) metallic spin glasses both with and without the presence of weak Dzyaloshinskii-Moriya anisotropy (DM). Finite-size scaling analyses of the data for equilibrium averages and relaxation times indicate a zero-temperature critical point for the isotropic RKKY model. When the DM interaction is included, the model exhibits a phase transition at a non-zero temperature. The values of the critical exponents at this transition are close to those obtained for the three-dimensional short-range Ising spin glass and in experiments on CuMn.

Distribution of Yang-Lee Zeros of the ±JIsing Model

A numerical technique to find out the distribution of the zeros of the partition function in the complex field plane is presented for the lsing model with arbitrary nearest-neighbor interactions. We apply it to the symmetric ± J model in two and three dimensions and obtain the distribution of the zeros of the effective partition function whose zeros in the complex field plane determine the analytical properties of the configuration-averaged free energy. Making use of the results, we discuss some problems of the short-range spin glass model including the existence of the Griffiths singularity and the AT line.

Percolation of order in frustrated systems: The dilute

The ``nodes-links-blobs'' description of percolation and real-space renormalization-group ideas are applied to the short-range Ising spin glass at T=0 with bond probability distribution P(J)=(1-p)\ensuremath{\delta}(J)+p[(1-q)\ensuremath{\delta}(J-1)+q\ensuremath{\delta}(J+1)]. The transition from paramagnet to spin glass is found to occur at ${p}^{\mathrm{*}}$g${p}_{C}$, with ${p}^{\mathrm{*}}$-${p}_{C}$\ensuremath{\sim}qln(1/q) for q\ensuremath{\ll}1.

Some comments on the Sherrington-Kirkpatrick model of spin glasses

In this paper the high-temperature phase of general mean-field spin glass models, including the Sherrington-Kirkpatrick (SK) model, is analyzed. The free energy in zero magnetic field is calculated explicitly for the SK model, and uniform bounds on quenched susceptibilities are established. It is also shown that, at high temperatures, mean-field spin glasses are limits of short-range spin glasses, as the range of the interactions tends to infinity.

Absence of many states in realistic spin glasses

Based on a simple scaling ansatz, the authors argue that no pure thermodynamic states other than the paramagnetic state and a pair of states in zero magnetic field which are related by a global spin flip can exist in short-range Ising spin glass models in any dimension. An analogous result should hold for XY and Heisenberg spin glasses, as well as for square-integrable long-range interactions.

Hidden valley structure of Ising spin glasses

The hidden valley structure of the phase space of short-range spin glasses is investigated. In the spirit of a similar investigation for liquids by Stillinger and Weber, valleys are defined as the set of states which by steepest descent lead to the same metastable state. The lifetime of valleys and the size of spin clusters involved in intervalley transitions on thermal Monte Carlo trajectories are calculated as a function of temperature.

Anisotropy-induced phase transition in metallic spin-glass alloys.

The critical behavior of the classical Ruderman-Kittel-Kasuya-Yosida model of metallic spin glasses in the presence of weak Dzyaloshinskii-Moriya--type anisotropy is studied by Monte Carlo simulations. Finite-size scaling analysis of the data for equilibrium averages and relaxation times indicates a finite-temperature phase transition. The values of the critical exponents are close to those obtained for the three-dimensional short-range Ising spin glass and in experiments on CuMn.