Freeman J. Dyson

Existence of a phase-transition in a one-dimensional Ising ferromagnet

AbstractExistence of a phase-transition is proved for an infinite linear chain of spins μj=±1, with an interaction energy

The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics

H = - \sum J(i - j)\mu _i \mu _j ,

CORRELATIONS BETWEEN EIGENVALUES OF A RANDOM MATRIX.

whereJ(n) is positive and monotone decreasing, and the sums ΣJ(n) and Σ (log logn) [n3J(n)]−1 both converge. In particular, as conjectured byKac andThompson, a transition exists forJ(n)=n−α when 1 < α < 2. A possible extension of these results to Heisenberg ferromagnets is discussed.

The Oklo bound on the time variation of the fine-structure constant revisited

Preface 1. The New Physics: a synthesis 2. The renaissance of general relativity 3. The inflationary universe 4. The edge of spacetime 5. Quantum gravity 6. The new astrophysics 7. Condensed matter physics in less than three dimensions 8. Critical point phenomena: universal physics at large length scales 9. Low temperature physics, superconductivity and superfluidity 10. Quantum optics 11. Physics of far-from-equilibrium systems and self-organisation 12. What is chaos, that we should be mindful of it? 13. Conceptual foundations of quantum mechanics 14. The quark structure of matter 15. Grand unified theories 16. Effective quantum field theories 17. Gauge theories in particle physics 18. Overview of particle physics Glossary Index.

Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions

Using mathematical tools developed by Hermann Weyl, the Wigner classification of group‐representations and co‐representations is clarified and extended. The three types of representation, and the three types of co‐representation, are shown to be directly related to the three types of division algebra with real coefficients, namely, the real numbers, complex numbers, and quaternions. The authors theory of matrix ensembles, in which again three possible types were found, is shown to be in exact correspondence with the Wigner classification of co‐representations. In particular, it is proved that the most general kind of matrix ensemble, defined with a symmetry group which may be completely arbitrary, reduces to a direct product of independent irreducible ensembles each of which belongs to one of the three known types.

A model for the origin of life

The two-player Iterated Prisoner’s Dilemma game is a model for both sentient and evolutionary behaviors, especially including the emergence of cooperation. It is generally assumed that there exists no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards. Here, we show that such strategies unexpectedly do exist. In particular, a player X who is witting of these strategies can (i) deterministically set her opponent Y’s score, independently of his strategy or response, or (ii) enforce an extortionate linear relation between her and his scores. Against such a player, an evolutionary player’s best response is to accede to the extortion. Only a player with a theory of mind about his opponent can do better, in which case Iterated Prisoner’s Dilemma is an Ultimatum Game.

Stability of Matter. II

Exact analytical expressions are found for the joint probability distribution functions ofn eigenvalues belonging to a random Hermitian matrix of orderN, wheren is any integer andN→∞. The distribution functions, like those obtained earlier forn=2, involve only trigonometrical functions of the eigenvalue differences.

Feynman’s proof of the Maxwell equations

Abstract It has been pointed out by Shlyakhter that data from the natural fission reactors which operated about two billion years ago at Oklo (Gabon) had the potential of providing an extremely tight bound on the variability of the fine-structure constant α. We revisit the derivation of such a bound by (i) reanalyzing a large selection of published rare-earth data from Oklo, (ii) critically taking into account the very large uncertainty of the temperature at which the reactors operated, and (iii) connecting in a new way (using isotope shift measurements) the Oklo-derived constraint on a possible shift of thermal neutron-capture resonances with a bound on the time variation of α. Our final (95% C.L.) results are: −0.9 × 10 −7 α Oklo − α now )/ α −7 and −6.7 × 10 −17 yr −1 α dot averaged /α −17 yr −1 .