Theory Of Spin Glasses Research Articles

Magnetic behavior of the Co2−xZnxTiO4 and Co2SnO4 systems

Our ac susceptibility (χ) measurements, carried out between 1.7 and 100 K, show five χ peaks, signaling five transition temperatures, in the disordered frustrated spinel ferrite Co2TiO4. This result, in conjunction with the replica symmetric mean field theory of vector spin glasses and earlier magnetization and neutron diffraction studies, indicates a separate freezing of A- and B-site spins. To our knowledge, such a phenomenon has not been observed before. Co2SnO4 and Co1.2Zn0.8TiO4 χ measurements, where three and one χ peaks are respectively observed, support this picture.

Mean-field theory of spin-glasses with finite coordination number.

The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.

On Spin Glass Theory

In this paper I present the progress that have been made in the theory of spin glasses (and related problems) in last years; the physical meaning of replica symmetry breaking is explained and some of the open problems are briefly discussed.

Anisotropic Spin Glass Behavior of Mn3+: Fe2TiO5 System

A decrease of both the longitudinal and transverse spin freezing temperatures occurs in the uniaxially anisotropic spin glass Fe2TiO5 when 5% of Fe3+ ions are replaced by Mn3+. This is understood on the basis of the mean field theory of anisotropic spin glasses, the increase in bond disorder on Mn3+ doping and the presence of weak, random Dzyaloshinsky-Moriya interaction which couples the longitudinal and transverse irreversibilities.

Spin glasses theory

We present the progress that has been made in the mean field theory of spin glasses and we explain the physical meaning of broken replica symmetry.

Spin glasses: Experimental facts, theoretical concepts, and open questions

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

The low temperature specific heat of Gd-Cu-Y metallic glasses

The specific heat of a series of amorphous aloys of composition Gd x Cu 0.37Y 0.63− x with 0 ⩽ x ⩽ 0.63 has been measured in the temperature range 2 to 50 K. A magnetic contribution to the specific heat is apparent in all the samples and has been determined with fair accuracy by subtracting the specific heat of corresponding nonmagnetic amorphous samples prepared with Lu rather than Gd. A qualitative study of the low field ac susceptibility of the magnetic samples has also been made. Samples with less than 35 at% Gd appear to be spin glasses, the results being qualitatively in accord with the predictions of the cluster mean field theory of concentrated spin glasses. As the Gd concentration is increased above 35 at% the samples behave increasingly like ferromagnets. However additional evidence from magnetisation measurements shows that even the sample with the highest concentration of Gd is not a simple ferromagnet.

Mean-field theory of the Ashkin-Teller spin glass.

The Gaussian-distributed random-bond Ashkin-Teller model on a Cayley tree is studied in the limit of infinite coordination number. This study is based on the relationship between the properties of the system defined on the usual Cayley tree and those of the system defined on a related hierarchical tree, the so-called closed asymmetric tree (CAT). With exploration of the hierarchical nature of the CAT a real-space renormalization-group procedure is implemented to obtain the generalized Sherrington-Kirkpatrick (SK) equations. The phase diagrams in three particular cases are obtained by numerical analysis of the SK equations.

Theory of Spin Glass by the Method of the Distribution Function of an Effective Field

The theory of the random Ising model formulated in terms of the distribution function of the effective field in the pair and in the cluster approximations is reviewed. An integral equation for the distribution function is derived. The integral equation has a solution for the paramagnetic state, a solution for the ferromagnetic state, a solution for the antiferromagnetic state, and solutions for the spin glass state. The phase diagram, and the ground state energy and entropy are calculated. The ground state entropy of the model is shown to be a small positive quantity contrary to the Sherrington­ Kirkpatrick infinitely long-ranged model. The phase diagram derived from the cluster approximation well explains the experimental phase diagrams, in particular, of fcc spin glass and the spin glass of EupSr1-pS. The distribution function for the spin glass in the pair approximation at T=O with a continu­ ous distribution is obtained analytically. They are composed of a-functions or of a-functions and a quadratic continuous function. In this paper the treatment of random spin systems, especially of the spin glass problem by the method of the distribution function of the effective field developed by our group is reviewed. A cluster (pair, triangle, square, tetrahedron, etc.) is taken in a given lattice (square, triangle, simple cubic, hexagonal, face-centered cubic, etc.). An effective field with a distribution is assumed to be applied to each vertex of the cluster. The partition function of the cluster is calculated exactly in terms of these effective fields. Self-consistent relation leads to an integral equation for the distribution function of the effective fields. The solution of the integral equation gives the physical quantities, the phase diagrams and the ground state properties. We consider random Ising models on a given crystal lattice. The hamiltonian &, the density matrix p, and the free energy Fare given by

Dynamical Mean Field Theory of Spin Glasses and Their Phase Transitions in ac External Fields

4introduced in a soft-spin version of the model is analyzed by means of the diagrammatic method. Restricting ourselves to its lowest order (single-loop) approximation, we examine relaxational dynamics of the model spin glass and clarify nature of its phase transition in the presence of an ac external field. The results provide a new clue to ac nonlinear measurements on spin glasses.

The spin glass in an AC field

The author considers the dynamical theory for spin glasses developed by Sompolinsky (1981), Hertz (1983) and others. The additional relations between the freezing parameters and the anomalous response parameters in their theory are considered. The author compares the dynamical theory with the probability distribution method of the overlap of the magnetisation between two different states. Finally he discusses the susceptibility of the spin glass in an AC field with a small finite amplitude, and the results explain the experimental results qualitatively.

Dynamic and Static Aspects in the Theory of Itinerant Spin Glasses

AbstractA superfield formulation of the Langevin dynamics for itinerant‐electron spin glasses is developed. Before taking the quenched configuration average the field‐theoretical scheme involves the supersymmetry. For comparison the standard replica method combined with Bogolyubov's variational principle is used to get the statics. The spin‐glass transition temperature is calculated in the presence of spatial fluctuations as well as in the mean‐field limit.

'Ordered' spin glass: a hierarchical memory machine

Recent developments in the theory of spin glasses due to the discovery of the hierarchical structure of different degrees of freedom are used for the construction of Ising spin memory models. A new learning algorithm is proposed. This algorithm permits one to construct an 'ordered' spin glass and therefore to memorise an exponential number of hierarchically ordered images.

Coexistence of spin-glass and antiferromagnetic orders in the Ising system Fe0.55Mg0.45Cl2.

The low-temperature phase of the dilute Ising antiferromagnet ${\mathrm{Fe}}_{0.55}$${\mathrm{Mg}}_{0.45}$${\mathrm{Cl}}_{2}$ in zero field is studied by specific-heat, ac-susceptibility, and neutron-scattering experiments. We find that in this phase, spin-glass behavior and antiferromagnetic long-range order coexist. Such a mixed-order phase is predicted by the mean-field theory of reentrant spin-glasses, but has never been observed before.

Some developments in the theory of modulated order. I. The role of fluctuations in the axial next-nearest-neighbor Ising model and the relevance of the Thouless-Anderson-Palmer equation.

The general mean-field theory of systems with modulated order is extended so as to include nontrivial fluctuation effects through the use of the Kirkwood approximation. Application of the theory to the axial next-nearest-neighbor Ising (ANNNI) model reveals that fluctuations (1) decrease the size of the entire ordered region of the phase diagram, (2) decrease that fraction of the ordered region that is most highly modulated, and (3) suppress the reentrant parts of the modulated region that do survive. Physical reasons for this behavior are discussed. In addition, we note that our ANNNI mean-field equations turn out to be precisely the Thouless-Anderson-Palmer (TAP) equations of spin-glass theory despite a number of rather different assumptions made in deriving the TAP equations. Some of what this observation reveals about the TAP equations is discussed.

Spin-glass transition in a magnetic field

Abstract Studies of the spin-glass phase transition in the presence of magnetic fields are reviewed. Most of the theoretical results on the existence of such a transition and its properties are derived from the mean-field theory of spin glasses, which describes infinite-range systems. In this limit, there exists a line T c(H) which separates the region (T > T c(H)) of a unique equilibrium paramagnetic state and the region (T > T c(H)) where ergodicity is broken and the system is frozen in one of many equilibrium spin-glass states. The singularities in both equilibrium and non-equilibrium quantities at the finite-field transition are described. In vector spin glasses this transition is associated with the freezing of transverse degrees of freedom. However, weak random anisotropy may induce a cross-over to Ising behaviour if it is sufficiently strong compared to the magnetic field. In two-dimensional systems with short-range forces, and perhaps in three-dimensional systems as well, the spin-glass transition...

Renormalization theory for spin glasses based on eigenstates of the J matrix (invited)

We propose a renormalization scheme for spin glasses based on localized clusters associated with the eigenstates of the exchange matrix. These clusters are chosen as the block spins of the renormalization procedure and their interactions estimated. The interaction matrix of this new spin glass problem is then diagonalized to find clusters of clusters, and so on. The simplest estimate of the interactions predicts a phase transition for d>2. The successive levels of slow modes or clusters provide a direct description of the relevant metastable states and spin dynamics on a hierarchy of time scales.

Scaling in spin-glasses.

Many results of the mean-field theory of spin-glasses violate simple scaling laws, including the magnetic field dependence of the transition lines, crossover effects of random anisotropy, and critical behavior in the ordered phase. These violations arise from two dangerously irrelevant variables. Below eight dimensions some mean-field exponents change and at $d=6$ scaling is restored. Below $d=6$ all scaling laws should be valid implying that the critical properties of real spin-glasses should be simpler than in mean-field theory. Experimental consequences are discussed.

Free energy of a spin glass

We give the theory of a model spin glass of the Sherrington-Kirkpatrick type. Determining that the free energy is given by the potential function of a two-dimensional electrostatic medium, we find exact expressions for this quantity in terms of a multipole expansion of the charge distribution. We also obtain the internal energy, entropy, and specific heat in the form of explicit integrals over the multipole distributions. Pending the outcome of a quantitative investigation into the structure of these functions, here we discuss their properties in a qualitative way.

Dynamical mean-field theory of realistic spin glasses beyond independent-mode approximation. II. Effect of reaction field

For pt.I see J. Phys. C., vol.17, p.5049, 1984. The author extends the previous calculation on a dynamical mean-field theory of realistic spin glasses (Chowdhury and Mookerjee) so as to incorporate the effect of the reaction field. The 'ordering temperature' of a mode is shown to depend not only on the corresponding eigenvalue of the random matrix J but also on the structure of the whole spectrum.