Abstract.I chart the considerable changes in the status and conception of the Lenz-Ising model from 1920 to 1950 in terms of three phases: In the early 1920s, Lenz and Ising introduced the model in the field of ferromagnetism. Based on an exact derivation, Ising concluded that it is incapable of displaying ferromagnetic behavior, a result he erroneously extended to three dimensions. In the next phase, Lenz and Ising’s contemporaries rejected the model as a representation of ferromagnetic materials because of its (...) conflict with the new quantum mechanics. In the third phase, from the early 1930s to the early 1940s, the model was revived as a model of cooperative phenomena. I provide more detail on this history than the earlier accounts of Brush (1967) and Hoddeson, Schubert, Heims, and Baym (1992) and question some of their conclusions. Moreover, my account differs from these in its focus on the development of the model in its capacity as a model. It examines three aspects of this development: (1) the attitudes on the degree of physical realism of the Lenz-Ising model in its representation of physical phenomena; (2) the various reasons for studying and using it; and (3) the effect of the change in its theoretical basis during the transition from the old to the new quantum mechanics. A major theme of my study is that even though the Lenz-Ising model is not fully realistic, it is more useful than more realistic models because of its mathematical tractability. I argue that this point of view, important for the modern conception of the model, is novel and that its emergence, while perhaps not a consequence of its study, is coincident with the third phase of its development. (shrink)

This is the last in a series of three papers on the history of the Lenz–Ising model from 1920 to the early 1970s. In the first paper, I studied the invention of the model in the 1920s, while in the second paper, I documented a quite sudden change in the perception of the model in the early 1960s when it was realized that the Lenz–Ising model is actually relevant for the understanding of phase transitions. In this article, which is self-contained, (...) I study how this realization affected attempts to understand critical phenomena, which can be understood as limiting cases of (first-order) phase transitions, in the epoch from circa 1965 to 1970, where these phenomena were recognized as a research field in its own right. I focus on two questions: What kinds of insight into critical phenomena was the employment of the Lenz–Ising model thought to give? And how could a crude model, which the Lenz–Ising model was thought to be, provide this understanding? I document that the model played several roles: At first, it played a role analogous to experimental data: hypotheses about real systems, in particular relations between critical exponents and what is now called the hypothesis of scaling, which was advanced by Benjamin Widom and others, were confronted with numerical results for the model, in particular the model’s so-called critical exponents. A positive result of a confrontation was seen as positive evidence for this hypothesis. The model was also used to gain insight into specific aspects of critical phenomena, for example that diverse physical systems exhibit similar behavior close to a critical point. Later, a more systematic program of understanding critical phenomena emerged that involved an explicit formulation of what it means to understand critical phenomena, namely, the elucidation of what features of the Hamiltonian of models lead to what kinds of behavior close to critical points. Attempts to accomplish this program culminated with the so-called hypothesis of universality, put forward independently by Robert B. Griffiths and Leo P. Kadanoff in 1970. They divided critical phenomena into classes with similar critical behavior. I also study the crucial role of the Lenz–Ising model in the development and justification of these ideas. (shrink)

This is the second in a series of three papers that charts the history of the Lenz–Ising model (commonly called just the Ising model in the physics literature) in considerable detail, from its invention in the early 1920s to its recognition as an important tool in the study of phase transitions by the late 1960s. By focusing on the development in physicists’ perception of the model’s ability to yield physical insight—in contrast to the more technical perspective in previous historical accounts, (...) for example, Brush (Rev Modern Phys 39: 883–893, 1967) and Hoddeson et al. (Out of the Crystal Maze. Chapters from the History of Solid-State Physics. Oxford University Press, New York, pp. 489–616, 1992)—the series aims to cover and explain in depth why this model went from relative obscurity to a prominent position in modern physics, and to examine the consequences of this change. In the present paper, which is self-contained, I deal with the development from the early 1950s to the 1960s and document that this period witnessed a major change in the perception of the model: In the 1950s it was not in the cards that the model was to become a pivotal tool of theoretical physics in the following decade. In fact, I show, based upon recollections and research papers, that many of the physicists in the 1950s interested in understanding phase transitions saw the model as irrelevant for this endeavor because it oversimplifies the nature of the microscopic constituents of the physical systems exhibiting phase transitions. However, one group, Cyril Domb’s in London, held a more positive view during this decade. To bring out the basis for their view, I analyze in detail their motivation and work. In the last part of the paper I document that the model was seen as much more physically relevant in the early 1960s and examine the development that led to this change in perception. I argue that the main factor behind the change was the realization of the surprising and striking agreement between aspects of the model, notably its critical behavior, and empirical features of the physical phenomena. (shrink)

In this paper, we examine the history of the idea among physicists that there is a fundamental limit to physical measuring processes and that this limit is set by noise. In contrast to previous studies, that have focused on the realization of the existence of such a limit, we focus on the noise aspect of this history. In his monograph entitled Noise from 1954, the Dutch-American physicist and pioneer of noise Alder van der Ziel described how noise came to be (...) seen as of practical importance for measurements:The study of spontaneous fluctuations was primarily theoretical as recently as 1925. At that time it. (shrink)

After World War II, quite a few mathematicians, including Mark Kac, John von Neumann, and Nobert Wiener, worked on the physical problem of phase transitions, i.e. changes in the state of matter caused by gradual changes of physical parameters such as the condensation of a gas to a liquid and the loss of magnetization of a ferromagnet above a certain temperature. The significance of these mathematicians was not so much that they brought mathematical rigor to the theoretical description of the (...) phenomena,1 but that they applied their mathematical skills and tools to solve concrete mathematical problems encountered in the microscopic modeling of phase transitions. The present paper deals... (shrink)