Stable mean-field solution of a short-range interacting SO(3) quantum Heisenberg spin glass

We present a mean-field solution for a quantum, short-range interacting, disordered, SO(3) Heisenberg spin model, in which the Gaussian distribution of couplings is centered in an antiferromagnetic (AF) coupling J[over ]>0, and which, for weak disorder, can be treated as a perturbation of the pure AF Heisenberg system. The phase diagram contains, apart from a Néel phase at T=0, spin-glass and paramagnetic phases whose thermodynamic stability is demonstrated by an analysis of the Hessian matrix of the free-energy. The magnetic susceptibilities exhibit the typical cusp of a spin-glass transition.     

Quantum XY Spin-Glass Model with Ferromagnetic Couplings and Plane Dzyaloshinski-Moriya interactions

In the generalized quantum replica symmetric approximation, a quantum XY spin-glass model with ferromagnetic coupling and planar Dzyaloshinski-Mariya (DM) interactions is investigated theoretically. Entropy and specific heat are calculated numerically as well as spin self-interactions and spin-glass order parameters for spin S = 1. It is found that the doublecusp of the specific heat, which corresponds to the collinear ferromagnetic and the paramagnetic ferromagnetic transitions respectively, .coincides completely due to DM-anisotropy interactions. Additionally, the local susceptibility and the spontaneous magnetization are evaluated numerically.     

Spin-glass transition in a Kondo lattice with quenched disorder

We use the Popov-Fedotov representation of spin operators to construct an effective action for a Kondo lattice model with quenched disorder at finite temperatures. We study the competition between the Kondo effect and frozen spin order in Ising-like spin glass. We present the derivation of new mean-field equations for the spin-glass order parameter and analyze the effects of screening of localized spins by conduction electrons on the spin-glass phase transition.     

Mean-field renormalization group for the q-state clock spin-glass model

The mean-field renormalization group is used to study the phase diagrams of a d-dimensional q-state clock spin-glass model. We found, for q = 3 clock, the transition from paramagnet to spin glass is an isotropic spin-glass phase, but for q = 4 clock, the transition from paramagnet to spin glass is an anisotropic spin-glass phase. However, for q ⩾ 5 clock, the result of anisotropic spin-glass phase depends on the temperature and the distribution of random coupling. While the coordinate number approaches infinity, the critical temperature evaluated by the mean-field renormalization group method is equal to that by the replica method.     

Monte Carlo simulation of a random-field Ising antiferromagnet

Phase transitions in the three-dimensional diluted Ising antiferromagnet in an applied magnetic field are analyzed numerically. It is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second-order phase transition to first-order transition to a new phase characterized by a spin-glass ground state and metastable energy states at finite temperatures.     

Exchange bias effect in partially oxidized amorphous Fe-Ni-B based metallic glass nanostructures

The magnetic properties of amorphous Fe-Ni-B based metallic glass nanostructures were investigated. The nanostructures underwent a spin-glass transition at temperatures below 100 K and revealed an irreversible temperature following the linear de Almeida-Thouless dependence. When the nanostructures were cooled below 25 K in a magnetic field, they exhibited an exchange bias effect with enhanced coercivity. The observed onset of exchange bias is associated with the coexistence of the spin-glass phase along with the appearance of another spin-glass phase formed by oxidation of the structurally disordered surface layer, displaying a distinct training effect and cooling field dependence. The latter showed a maximum in exchange bias field and coercivity, which is probably due to competing multiple equivalent spin configurations at the boundary between the two spin-glass phases.     

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.     

Quantum spin glass and the dipolar interaction

Anisotropic dipolar systems are considered. Such systems in an external magnetic field are expected to be a good experimental realization of the transverse field Ising model. With random interactions, this model yields a spin glass to paramagnet phase transition as a function of the transverse field. We show that the off-diagonal dipolar interaction, although effectively reduced, induces a finite correlation length and thus destroys the spin-glass order at any finite transverse field. We thus explain the behavior of the nonlinear susceptibility in the experiments on LiHo(x)Y(1-x)F(4), and argue that a crossover to the paramagnetic phase, and not quantum criticality, is observed.     

Phase Diagram of a Quantum Hopfield Spin Glass with the Pseudo-Inverse Rule

A quantum Ising spin-glass model in a transverse field is presented. The network is based on a modified version of the Hopfield spin glass. The equations for the order parameters describing the ordered phases are obtained, and the phase transitions of the system are analyzed. The ordered phases are suppressed by the existence of both quan turn effects and the random overlaps between the patterns.     

Quantum and thermal fluctuations in the SU(N) Heisenberg spin-glass model near the quantum critical point

We solve for the SU(N) Heisenberg spin glass in the limit of large N focusing on small S and T. We study the effect of quantum and thermal fluctuations in the frequency dependent response function and observe interesting transfers of spectral weight. We compute the T dependence of the order parameter and the specific heat and find an unusual T2 behavior for the latter at low temperatures in the spin-glass phase. We find remarkable qualitative agreement with various experiments on the quantum frustrated magnet SrCr(9p)Ga(12-9p)O19.     

Induced random fields in the LiHoxY1-xF4 quantum Ising magnet in a transverse magnetic field

The LiHoxY1-xF4 magnetic material in a transverse magnetic field Bx x perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in a random disordered system. We show that the Bx-induced magnetization along the x direction, combined with the local random dilution-induced destruction of crystalline symmetries, generates, via the predominant dipolar interactions between Ho3+ ions, random fields along the Ising z direction. This identifies LiHoxY1-xF4 in Bx as a new random field Ising system. The random fields explain the rapid decrease of the critical temperature in the diluted ferromagnetic regime and the smearing of the nonlinear susceptibility at the spin-glass transition with increasing Bx and render the Bx-induced quantum criticality in LiHoxY1-xF4 likely inaccessible.     

Spin glasses: Some recent experiments

This review of the spin-glass problem will begin by considering the basic ingredients of a spin glass. Then I shall summarize the fundamental experimental properties and the real systems which are being studied. A bit of theory will be presented to show how idealized the models are when compared to the real materials. Finally I shall discuss the dynamics of the spin-glass phase transition and relaxations within the frozen state, drawing upon the muon investigations wherever possible.     

Nonequilibrium dynamic effects within a quantum droplet model of Ising spin glass

The real and imaginary parts of the dynamic linear magnetic susceptibility at very low temperatures are found within the quantum droplet model of Ising spin glass, and their temperature and frequency dependences are calculated analytically and numerically. The nonequilibrium theory of the response of quantum-mechanical systems is used. The slow, quasi-equilibrium dynamics and the divergence of the dynamic linear susceptibility are investigated. Numerical calculations illustrate the crossover between the low-frequency and high-frequency regimes. A transition to the glasslike state is assumed to occur at a nonzero temperature. At zero temperature, the results are identical to those obtained earlier. The spin-glass ageing is considered briefly in the model at hand.     

Chiral-glass transition and replica symmetry breaking of a three-dimensional heisenberg spin glass

Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a finite-temperature chiral-glass transition without the conventional spin-glass order is established. Critical exponents characterizing the transition are different from those of the standard Ising spin glass. The calculated overlap distribution suggests the appearance of a peculiar type of replica-symmetry breaking in the chiral-glass ordered state.     

Pairwise Entanglement and Quantum Phase Transitions in Spin Systems

We examine several well-known quantum spin models and categorize the behaviour of pairwise entanglement at quantum phase transitions. A unitied picture on the connection between the entanglement and quantum phase transition in spin systems is presented.     

Fluctuation-dissipation ratio of the Heisenberg spin glass

The fluctuation-dissipation (FD) relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation. The numerically determined FD ratio exhibits a "one-step-like" behavior, the effective temperature of the spin-glass state being about twice the spin-glass transition temperature, T(eff) approximately 2T(g), irrespective of the bath temperature. The results are discussed in conjunction with the recent experiment by Hérisson and Ocio, and with the chirality scenario of the spin-glass transition.     

Dynamical response of quantum spin-glass models at t = 0

We study the behavior of two archetypal quantum spin glasses at T = 0 by exact diagonalization techniques: the random Ising model in a transverse field and the random Heisenberg model. The behavior of the dynamical spin response is obtained in the spin-glass ordered phase. In both models it is gapless and has the general form chi(")(omega) = qdelta(omega)+chi(")(reg)(omega), with chi(")(reg)(omega) approximately omega for the Ising and chi(")(reg)(omega) approximately const for the Heisenberg, at low frequencies. The method provides new insight to the physical nature of the low-lying excitations.     

First-order phase transition in easy-plane quantum antiferromagnets

Quantum phase transitions in Mott insulators do not fit easily into the Landau-Ginzburg-Wilson paradigm. A recently proposed alternative to it is the so-called deconfined quantum criticality scenario, providing a new paradigm for quantum phase transitions. In this context it has recently been proposed that a second-order phase transition would occur in a two-dimensional spin 1/2 quantum antiferromagnet in the deep easy-plane limit. A check of this conjecture is important for understanding the phase structure of Mott insulators. To this end we have performed large-scale Monte Carlo simulations on an effective gauge theory for this system, including a Berry-phase term that projects out the S=1/2 sector. The result is a first-order phase transition, thus contradicting the conjecture.     

Scaling analysis of domain-wall free energy in the Edwards-Anderson Ising spin glass in a magnetic field

The stability of the spin-glass phase against a magnetic field is studied in the three- and four-dimensional Edwards-Anderson Ising spin glasses. Effective couplings J(eff) and effective fields H(eff) associated with length scale L are measured by a numerical domain-wall renormalization-group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H --> 0 but remains finite for any nonzero H, implying that the spin-glass phase is absent even in an infinitesimal field. These results are well consistent with the droplet theory for short-range spin glasses.