Philip W. Anderson

Anomalous low-temperature thermal properties of glasses and spin glasses

Abstract We show that a linear specific heat at low temperatures for glass follows naturally from general considerations on the glassy state. From the same considerations we obtain the experimentally observed anomalous low-temperature thermal conductivity, and we predict an ultrasonic attenuation which increases at low temperatures. Possible relationships with the linear specific heat in magnetic impurity systems are pointed out. We suggest experimental study of the relaxation of thermal and other properties.

Theory of spin glasses

A new theory of the class of dilute magnetic alloys, called the spin glasses, is proposed which offers a simple explanation of the cusp found experimentally in the susceptibility. The argument is that because the interaction between the spins dissolved in the matrix oscillates in sign according to distance, there will be no mean ferro- or antiferromagnetism, but there will be a ground state with the spins aligned in definite directions, even if these directions appear to be at random. At the critical temperature the existence of these preferred directions affects the orientation of the spins, leading to a cusp in the susceptibility. This cusp is smoothed by an external field. Although the behaviour at low t needs a quantum mechanical treatment, it is interesting to complete the classical calculations down to t=0. Classically the susceptibility tends to a constant value at t=0, and the specific heat to a constant value.

Theory of dirty superconductors

Abstract A B.C.S. type of theory (see Bardeen , Cooper and Schreiffer , Phys. Rev. 108, 1175 (1957)) is sketched for very dirty superconductors, where elastic scattering from physical and chemical impurities is large compared with the energy gap. This theory is based on pairing each one-electron state with its exact time reverse, a generalization of the k up, − k down pairing of the B.C.S. theory which is independent of such scattering. Such a theory has many qualitative and a few quantitative points of agreement with experiment, in particular with specific-heat data, energy-gap measurements, and transition-temperature versus impurity curves. Other types of pairing which have been suggested are not compatible with the existence of dirty superconductors.

Resonating valence bonds: A new kind of insulator?

Abstract The possibility of a new kind of electronic state is pointed out, corresponding roughly to Paulings idea of “resonating valence bonds” in metals. As observed by Pauling, a pure state of this type would be insulating; it would represent an alternative state to the Neel antiferromagnetic state for S = 1/2. An estimate of its energy is made in one case.

A Structural Approach to Assessing Innovation: Construct Development of Innovation Locus, Type, and Characteristics

We take a structural approach to assessing innovation. We develop a comprehensive set of measures to assess an innovations locus, type, and characteristics. We find that the concepts of competence destroying and competence enhancing are composed of two distinct constructs that, although correlated, separately characterize an innovation: new competence acquisition and competence enhancement/destruction. We develop scales to measure these constructs and show that new competence acquisition and competence enhancing/destroying are different from other innovation characteristics including core/peripheral and incremental/radical, as well as architectural and generational innovation types. We show that innovations can be evaluated distinctively on these various dimensions with generally small correlations between them. We estimate the impact these different innovation characteristics and types have on time to introduction and perceived commercial success. Our results indicate the importance of taking a structural approach to describing innovations and to the differential importance of innovation locus, type, and characteristics on innovation outcomes. Our results also raise intriguing questions regarding the locus of competence acquisition (internal vs. external) and both innovation outcomes.

Solution of 'Solvable model of a spin glass'

Abstract The Sherrmgton-Kirkpatrick model of a spin glass is solved by a mean field technique which is probably exact in the limit of infinite range interactions. At and above T c the solution is identical to that obtained by Sherrington and Kirkpatrick (1975) using the n → O replica method, but below T c the new result exhibits several differences and remains physical down to T = 0.

Theory of Magnetic Exchange Interactions:Exchange in Insulators and Semiconductors

Publisher Summary This chapter discusses that the subject of exchange in magnetic materials is divided into two parts, referring to insulators and to metals. This distinction is useful from the magnetic point of view because in insulators the spins and magnetic moments whose alignments lead to magnetic effects are certainly localizable so that phenomenologically is described by a spin Hamiltonian that contains spin operators and exchange terms of Heisenberg type. It discusses that there is relationship among the mechanisms important in metals, such as conduction electron polarization, and those in insulators. The chapter provides historical discussion of the subjects of antiferromagnetism and of exchange in insulators. It focuses on the Heisenberg Hamiltonian, with a brief derivation and a discussion of some of the statistical theories of magnetism based upon it, primarily molecular field theory, which is by far the most generally useful in the experimental measurement of exchange. The chapter also describes older theories and presents ideas about super-exchange, and gives a discussion and a diagrammatic classification of all the possible higher-order processes.

The question of classical localization A theory of white paint

Abstract The expected behaviour of localizing media for classical wave propagation is analysed. Some possible examples in electromagnetic and acoustic phenomena are given.

On the ground state properties of the anisotropic triangular antiferromagnet

Abstract Our aim is to present further evidence supporting a recent suggestion by Anderson (1973) that the ground state of the triangular antiferromagnet is different from the conventional three-sublattice Neel state. The anisotropic Heisenberg model is investigated. Near the Ising limit a peculiar, possibly liquid-like state is found to be energetically more favourable than the Neel-state. It seems to be probable that this type of ground state prevails in the anisotropy region between the Ising model and the isotropic Heisenberg model. The implications for the applicability of the resonating valence bond picture to the S = ½ antiferromagnets are also discussed.

What mad pursuit : a personal view of scientific discovery

* Introduction * Prologue * The Gossip Test * The Baffling Problem * Rocking the Boat * The a Helix * How to Live with a Golden Helix * Books and Movies About DNA * The Genetic Code * Fingerprinting Proteins * Theory in Molecular Biology * The Missing Messenger * Triplets * Conclusions * Epilogue: My Later Years