R. N. Bhatt

A scaling method for low temperature behavior of random antiferromagnetic systems (invited)

Low temperature properties of random antiferromagnetic Heisenberg spin‐1/2 systems with a wide distribution of exchange couplings are examined using a scaling technique. The method iteratively discards the irrelevant high energy excitations of strongly coupled clusters, while retaining the low lying states which are reproduced by an equivalent smaller cluster. The method is applied to n‐doped semiconductors, a spatially random three dimensional system of spin‐1/2 donors with Heisenberg exchange varying exponentially with separation. It shows how the system does not order down to temperatures well below the median nearest neighbor exchange. Comparison is made with the corresponding system in two dimensions and the one‐dimensional random antiferromagnetic chain (applicable to certain organic charge transfer salts), as well as with the case of Ising spins in three dimensions.

Impurity states and magnetic order in layered copper oxides (invited)

The influence of impurity potentials on vacancies in the t‐J model is studied through the exact diagonalization of systems with 8 and 16 sites. For a wide range of model parameters, the ground state transforms according to the two‐dimensional vector representation of C4v and has S =1/2. The inclusion of symmetry breaking effects present for an isolated impurity in an infinite system yields an anisotropic ground state which may couple to local lattice distortions. Implications for magnetic order, spectroscopy, and the metal‐insulator transition in the CuO2 planes of the cuprate superconductors are discussed. The relationship to the behavior of free vacancies and the role of finite size effects are considered. A mean‐field Hubbard model analysis is proposed as a supplementary approach.

Magnetic properties across the metal‐insulator transition (invited)

We review recent theoretical and experimental work on the metal to insulator transition in doped semiconductors. The spin excitations on the insulating side of the transition can be described in terms of a spin‐ 1/2 Heisenberg antiferromagnet with the spins randomly located in space. Numerical analysis of this Hamiltonian has led to a fairly complete understanding of the static spin susceptibility and the electron spin resonance spectrum. The physics on the metallic side far from the transition is also fairly well understood in terms of a recently developed theory of the disordered Fermi liquid. The physics near the transition point is, however, still not clear. All the experimental evidence indicates the presence of local electronic moments on the metallic side of the transition. Recent theoretical work and open problems in the description of such a metallic phase are briefly discussed.

Spin dynamics across the metal‐insulator transition

A theoretical study of the dynamics of electron spins in disordered insulators and metals is performed. Spin diffusion is found to slow down at low temperatures, making the system unusually sensitive to spin‐dependent perturbations. This sensitivity shows up in an unusual frequency and temperature dependence of the linewidth and resonance field of the electron spin resonance (ESR) signal. These results are used to interpret recent ESR measurements in phosphorus doped silicon in both the insulating and metallic phases, and good agreement is obtained with experiment.

The four dimensional Ising spin glass: A Monte Carlo study (invited)

We describe results of Monte Carlo simulation studies on the Ising spin glass in four dimensions on a hypercubic lattice with nearest neighbor bonds. Studies of the equilibrium static properties show that the system undergoes a genuine phase transition to an ordered spin glass phase. Critical dynamical behavior is analyzed to obtain the dynamic exponent. Finally, we describe results on the spin glass phase, in particular the finite size scaling of the order parameter distribution function, and compare it with existing models of the spin glass phase, namely the droplet model and the Parisi solution for the low temperature phase of the infinite range spin glass.

Order parameter distribution of the random bond Ising ferromagnet with antiperiodic boundary conditions

The two‐dimensional random bond Ising ferromagnet with antiperiodic boundaries in one direction has been studied by Monte Carlo simulations. From the overlap distribution function P(q), the scaling behavior of P(q) near q=0 with linear dimension L has been obtained. In contrast to recent simulations of the four‐dimensional Ising spin glass, our results are consistent with the predictions of the droplet model.