Dynamics of the infinite-range ising spin glass

The Glauber dynamics of an Ising spin glass with infinite-range interactions and additional static field, h, is investigated near the freezing temperature, T_f. We obtain critical slowing down at and below the de Almeida-Thouless instability line, h_c(T), to order (1?T/T_f)³ with algebraic decay of the spin correlations ～t^?ν, where $\text{ν=}\text{1}\text{2}$ at T_f and $\text{ν≤}\text{1}\text{2}$ for T<T_f.     

Effect of local anisotropy on spin glass

The effects of uniaxial crystal field on spin glass properties are investigated. The parallel susceptibility (χ∥) exhibits sharper cusp than the perpendicular one (χ⊥).     

On the strict inequality between quenched and annealed ising spin glass

Using the cluster expansion technique, we estimate, uniformly in the volume, the difference between the quenched and annealed free energy in the high temperature phase of ad-dimensional Ising spin glass model with Bernoulli couplings.     

Interface energies in ising spin glasses

The replica method has been used to calculate the interface free energy associated with the change from periodic to antiperiodic boundary conditions in finite-dimensional spin glasses. At mean-field level the interface free energy vanishes, but after allowing for fluctuation effects, a nonzero interface free energy is obtained which is significantly different from numerical expectations.     

Magnetic correlations in three-dimensional ising spin glasses

By a recursive method numerically exact free energies are calculated forL×L×M Ising lattices with random bonds andL=4, 4M10, applying free boundaries in the direction where the lattice is less small and otherwise periodic boundary conditions. Both for the±J model and the gaussian model the specific heat is in fair agreement with Monte Carlo results obtained for much larger lattices. However, the correlation function [S ₀ S _{R T} ² ]_av is found to decay exponentially with distanceR [for 1R9] at temperatures far below the apparent freezing temperatures of the Monte Carlo simulations, implying that there is no nonzero Edwards-Anderson order parameter in equilibrium. This behavior is qualitatively different from Mattis spin glasses (or Ising ferromagnets) where even smaller lattices show pronounced magnetic order at low temperatures. As the Monte Carlo results give evidence for a nonzero Edwards-Anderson order parameter (for not too long observation times), which is fairly independent of lattice size down to sizes of 4³, we suggest that Edwards-Anderson ordering is a nonequilibrium phenomenon visible only in studying dynamic properties.     

GKS inequalities for arbitrary spin ising ferromagnets

Elementary proofs of the first and second Griffiths-Kelly-Sherman (GKS) inequalities are given for higher-spin Ising systems with a Hamiltonian containing only a quadratic form in the spin variables and integer powers of single spin variables. These proofs are obtained using Gaussian random variables. A slight generalization of previous results has been obtained in that the coefficients of the even powers of the spin variables are allowed to be negative.Work supported by NSF Grant GP-36564X.     

Numerical study of metastable States in ising spin glasses

We study numerically the structure of metastable states in the Sherrington-Kirkpatrick spin glass. We find that all nonparamagnetic stationary points of the free energy are organized into pairs, consisting of a minimum and an order 1 saddle, which coalesce in the thermodynamic limit. Within the annealed approximation, the entropic contribution of these states, that is the complexity, is compatible with the supersymmetry-breaking calculation performed by Bray and Moore [J. Phys. C 13, L469 (1980)]]. This result indicates that the supersymmetry is spontaneously broken in the Sherrington-Kirkpatrick model.     

Block spin techniques applied to the ising model

A detailed study of the critical behaviour of the Ising model in 1+1 and 2+1 dimensions is made using an approximate real space renormalization transformation which involves block spins. The critical indices α, β, η, and ν are calculated and compared with previous results, as is the critical couplingy _c. The method is shown to respect one of the scaling relations, and in 1+1D some exact results are reproduced (y _c=1, ν=1).     

Quantum HeisenbergS=1 spin glass: Effect of anisotropy and ferromagnetic interaction

A complete analysis of the transfer dynamics in an asymmetric nonlinear dimer model with different cubic site polarizations is given. The analysis is performed for both the dynamics of the full density matrix on the Bloch sphere (location of fixed points, bifurcation in dependence on the polarization strength) and of the reduced space of the occupation difference using a potential function. For a time dependent harmonic perturbation the appearance of chaotic transfer regimes near a homoclinic structure on the Bloch sphere is demonstrated. A comparison with spin models is performed. It is shown that the chaotic regime corresponds to chaotic motion in a classical spin model witha–S _z ² nonlinearity and an external magnetic field having its constant and time dependent parts in the same direction.     

Contribution to the theory of mixed ising spin systems

An effective-field theory of mixed spin—1/2 and spin-1 Ising system with random bond and crystal-field interactions is developed. The general expressions for evaluating the thermodynamic quantities are obtained. In the last section, transition temperature and tricritical behavior are examined for the mixed ferromagnetic spin system withz=3, wherez is the coordination number. The obtained results are reasonable in comparison with exact and approximate ones. Owing to the simplicity, the present method can be applied to a wide class of the random systems.     

Dipolar interactions and origin of spin ice in ising pyrochlore magnets

Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the nearest-neighbor "spin ice" model. We discuss the dipolar energy scale present in both these materials and discuss how spin-ice behavior can occur despite the presence of long-range dipolar interactions. We present results of numerical simulations and a mean field analysis of Ising pyrochlore systems. Based on our quantitative theory, we suggest that the spin-ice behavior in these systems is due to long-range dipolar interactions, and that the nearest-neighbor exchange in Dy2Ti2O7 is antiferromagnetic.     

Spectrum of relaxation times for ising spin clusters in random fields

Summary Exact results on the single-spin-flip Glauber dynamics of six-coupled random field Ising spins with the coordination number of four are presented. Two distributions of random fields (RF), binary (BD) and Gaussian (GD) ones, are investigated. The effects of the static magnetic field are discussed. In the zero-magnetic-field case, the number of diverging relaxation times is equal to the number of energy minima minus one. This rule breaks in the presence of a magnetic field. The longest relaxation times in the absence of the field verify the Arrhenius law with the energy barrier determined by the energy needed to invert the ground-state spin configuration. At low temperature, according to the Arrhenius law, the spectrum of relaxation times shows a two-peaked distribution on a logarithmic scale. In the GD case of RF, the energy barrier distribution is continuous, while it is quasi-discrete in the BD case.     

Random anisotropy in lattice gas model

We consider a lattice-gas model with infinite-range interaction with site dependent random anisotropy distributed with a Gaussian distribution. The random anisotropy lattice-gas analogous of the random field Ising model is solved exactly using a replica theory. We show that, at finite temperature, the introduction of disorder eliminates completely the phase transition, and destroy the equivalence between real gases and Ising magnets. Whereas at T = 0, the density of occupied sites has a step-like behavior as function of the random anisotropy.