II. Some Aspects of the Recent Development of Atomic Theory

Michael Ellis Fisher

The aim of this contribution is to draw attention to some recent developments in the theory of critical phenomena and phase transitions that may be of interest to the magnetism community in that magnetic systems have provided a fertile testing ground for modern theoretical ideas concerning ordering and phase transitions while, on the other hand, many aspects of observed magnetic phase behavior have required sophisticated theory for their proper elucidation. The new works in question have been published or will appear shortly: accordingly, only an outline is presented here together with references to the main literature sources which, in turn, include fuller references to earlier work not explicitly mentioned. Four linked topics are addressed: (i) finite-size effects at first-order transitions; (ii) asymptotic degeneracy in transfer matrices, which is intimately related to long-range order; (iii) some consequences of the conformal covariance of fluctuations at a critical point in bulk and in finite systems, especially in two spatial dimensions; (iv) the discovery of ‘‘exactly soluble’’ two-dimensional models exhibiting two infinite classes of distinct critical and multicritical points.

PROF. J. K. ROBERTSON, professor of physics, Queen's University, Kingston, Ontario, in his presidential address to the Royal Society of Canada de-livered on May 21, 1945, argues that the notions of continuity and discontinuity as used in physics and other sciences are complementary and not just contradictory. When, in the eighteenth century, physical theory was occupied with the continuous aspect of things it was natural to suppose that the structure of the world must be either continuous or discontinuous, not both. Therefore, since continuity was apparent, there could be no discontinuity anywhere, as Leibniz argued. The chemical atomic theory and the kinetic theory of gases of the nineteenth century brought out the aspect of discontinuity for the first time, and recent sub-atomic physics has gone a stage further. At every stage, however, as Prof. Robertson emphasizes, theory really requires both continuity and discontinuity. This was first realized in the case of light, which in some aspects is continuous, and in others discontinuous ; and, later, electrons were found to play a similar dual part. Granted that the single electron is discrete, indefinite and indeterminate, it should not be inferred that the continuity, definiteness and strict causality found in the behaviour of large numbers of electrons are not equally genuine aspects of the physical world. Prof. Robertson refers briefly to the way in which the biological theory of evolution requires both a continuous long-term aspect and a discontinuous short-term one ; and he ends by asking the question, whether new discoveries in science which look like discontinuities in the historical development of thought are not also in other respects examples of the continuity of thought.

Gérard G. Emch

Abstract This paper contains the skeleton of one lecture, and of two raporteur's interventions, made at the Sanibel Symposium in February–March, 1979. The task asked of this lecturer was to present an outline of the program of nonequilibrium statistical mechanics, and to indicate some of the recent developments in our understanding of this program. Section I lists a few of the principal physical ingredients of the theory. The possible implementation of certain aspects of the program is demonstrated in Sec. II with the help of three exactly soluble models. Finally in Sec. III we extrapolate from these particular examples in two directions: the stochastic aspect of statistical mechanics, and some remarks on the theory of the quantum measurement process. The presence, at the Symposium, of several distinguished lecturers who presented their own original, and most interesting, contributions hopefully made appear less outrageous—at least at the time—the severe omissions due to the personal choices this particular speaker had to make to keep within the time limitations inherent to such a gathering. It is now hoped that, even when taken out of the full context of the Symposium, the rearranged text which follows might nevertheless help focusing attention on some of the important problems remaining to be solved. It is a pleasure to acknowledge here the stimulating hospitality of the Symposium Scientific Director, Professor P.‐O. Löwdin.

Jagdish Mehra, Helmut Rechenberg