A Mookerjee

Mean-field theories of spin glasses

Different kinds of mean-field theories (MFT) of spin glasses (SG) are reviewed. A brief introductory review of major experimental results, which have to be explained theoretically, is presented in the beginning. Marshall-Klein-Brout type random local field theories are described qualitatively. Edwards-Anderson MFT of SG transition is introduced after defining the various relevant order parameters. Almost all the static and dynamic approaches to the solution of the Sherrington-Kirkpatrick model are reviewed in detail. The existence of mixed phase(s) in the MFT of vector SG is examined critically in the light of recent theories and experiments. The existence of macroscopic anisotropy energy in SG and their microscopic origin are mentioned. The upper and lower critical dimensionalities obtained by different authors are enlisted. The concept of frustration and its deeper connection with other branches of human knowledge are indicated. Nonlinear susceptibilities, spin wave and relaxational modes in SG are also reviewed. The two-level-system picture of SG, its physical basis and important consequences are presented. The Tholence-Tournier-Wohlfarth phenomenological cluster model of SG is discussed with a stress on the role of measurement time. SG transition has been described as percolation and localization-delocalization problems. Some special features of the local field distribution in SG are mentioned. Some results of computer simulation on the various models of SG are summarized. The theories of the transport properties of SG are enlisted. Recent trends in the theory of SG are indicated at the end.

A mean-field, effective medium theory of random magnetic alloys. II. The random heisenberg model

A classical Heisen berg model is analysed. The interaction is of the RKKY type and only between sites randomly occupied by magnetic atoms. The possible phases are described at various temperatures and concentration of magnetic atoms. The procedure is realistic and not the ‘exactly’ solvable kind studied by earlier workers.

On the augmented-space cluster coherent-potential approximation and its analytic properties

The authors discuss the analytic properties of the configuration-averaged Green function obtained using the self-consistent cluster coherent-potential approximation, developed in the augmented-space formalism. It is shown that the iteration scheme for the self-energy is always convergent to a unique value, which is bounded and herglotz, provided one starts off with a bounded and herglotz guess. This ensures that one shall always get a unique, non-negative density of states at all energies.

Magnetic behaviour of spin-glass alloys beyond the percolation concentration

Using a mean-field effective medium approach, the authors study the phase diagram of a random Heisenberg model. In particular they study the phases and magnetisation beyond the percolation limit, and compare these with the experimental observations in AuFe alloys with high concentrations of Fe.

A mean-field, effective medium theory of random binary alloys III. The ising model with competing interactions

The Ising model with competing interactions is studied in a mean field effective medium approach. The phase diagram of such model alloys is studied. We conclude that for all ratios of the competing interaction moments, a spin glass phase always exists at low temperatures for certain concentration regimes.

Magnetic properties of Ni-Mo single-crystal alloys; theory and experiment

The magnetizations of single crystals with x = 4, 6, 8 and 10% by weight have been measured at 4.2 K using a vibrating-sample magnetometer and a superconducting quantum interference device (SQUID). The magnetizations of the alloy at these low concentrations and at 0 K have been theoretically determined by using the tight-binding linearized muffin-tin orbital method coupled with augmented-space recursion. The theoretical data are compared with the experiment.

Cluster generalisation of the KKR coherent potential methods for random metallic alloys

A generalisation of the single-site KKR-CPA to include effects of clustering is presented here. The formalism combines the usual KKR ideas with the augmented space formalism introduced by the author.

Relation between Wohlfarth's model and the percolation model of spin glasses

The mathematical relation between Wohlfarths model and Mookerjee and Chowdhurys percolation model of spin glasses and its physical meaning are discussed.

Electrical and magnetic properties of AuFe alloys

We study the electronic and magnetic structure of AuFe alloys for varying Fe concentrations. The basis of our study is the augmented-space recursion in conjunction with the local spin-density approximation. We study magnetism from an itinerant-electron viewpoint and show that at low Fe concentrations the random phase arrangement is the more stable phase at T = 0 K as compared to the ferromagnetic, antiferromagnetic and paramagnetic arrangements. At higher concentrations the ferromagnetic arrangement becomes the most stable but the average moment decreases with increasing Au concentration.

Logarithmic relaxation of magnetisation in the percolation model of the spin-glass transition

The authors show that, because of the existence of a distribution of relaxation times in the percolation model of the spin-glass transition, magnetisation relaxes logarithmically in time.