The now-famous model was considered by Ernst Ising in his doctoral dissertation, as suggested by his supervisor Wilhelm Lenz. It was originally intended to explain the physical phenomenon — onset of a ferromagnetic phase — by the theory arising solely from the local interactions between elementary magnetic moments of individual atoms. The work of Lenz and Ising marked the start of a scientific direction that, over nearly 100 years, delivered extraordinary successes in explaining collective behaviour in a vast variety of systems both within and beyond the natural sciences.Today, the Ising model is of ubiquitous importance in theoretical and condensed matter physics, and is also fundamental, in its various modifications in complex system science. This model is paradigmatic as it helps to find a common language for scientists from diverse fields of knowledge, ranging from natural sciences to social sciences, economics and even humanities.The purpose of this book is to present the original German version of the dissertation (as preserved in the Library of the University of Hamburg), together with its English translation and extended commentary, especially regarding the later developments concerning the change in the microscopic basis of the model. We also present a biography of Ernst Ising, as he lived a unique life of almost a century, surviving the Nazi occupation of Europe and later returning to teaching in the USA.
