The atoms which constitute a solid consist of nuclei and electrons. For a description of the state of the solid it is not, however, necessary to spec… - Rudolf Peierls

When I arrived in Leipzig, Heisenberg was working on the theory of ferromagnetism. It was known the magnetism of such substances as iron was due to the "spin" of the electrons inside the substance. Each electron spins like a little top, and in the iron there is a "molecular field", a force that tends to align the spin of each electron with that of its neighbors. But the nature of this field was unknown. It could not be a magnetic effect because magnetic forces are much too weak to account for the observed behaviour. Heisenberg saw that the answer lay in the Pauli exclusion principle, which says that no two electrons can be in exactly the same state. Thus two electrons with the same spin orientation keep out of each other's way; while this repulsion may increase their energy of motion, it diminishes their mutual repulsion, and can therefore lead to a decrease in total energy, making the parallel alignment of the electron spins energetically favourable. He had encountered this mechanism in the theory of atomic spectra and concluded that it was also responsible for ferromagnetism.

His contributions to condensed matter physics were largely on fundamental questions, establishing the principles of this subject. Most of this work was done during the years 1928–37, but much of it could not be tested until the experimental techniques needed for this had become sufficiently developed. ...
Rudolf Peierls's work in nuclear physics began in 1933, when James Chadwick challenged him and Hans Bethe to explain his first measurements of the cross-section for photo-disintegration of the deuteron. Peierls's experience in this field developed rapidly within the next few years, on both practical questions and academic research, to the point where he and Otto Frisch could confidently conclude that the construction of an atomic bomb would be quite possible using ²³⁵U, which could be obtained obtained from natural uranium by a feasible separation process, and they pointed this out in the famous Frisch-Peierls Memorandum of 1940 which they sent to the British government. This led to the Atomic Bomb Project, at first in Britain under the name "Tube Alloys Project" and later in USA as the "Manhattan District Project", which many of the UK scientists, including both Peierls and Frisch, were sent to join at the end of 1943.

After the war, Bethe went back to Cornell, where he helped build an outstanding research center in high-energy physics. Peierls returned to Birmingham, where he created the outstanding school of theoretical physics in Western Europe. The two physicists established a pipeline between the two institutions and offered their generous evaluations of the young postdocs and colleagues—Hugh McManus, Edwin Salpeter, Stuart Butler, Richard Dalitz, Freeman Dyson, and others—that they sent to one another. Their correspondence likewise gives perceptive overviews of advances in high-energy physics, especially of the progress made after 1955 in the nuclear many-body problem on which Bethe was concentrating. Their letters also concern policy challenges posed by, for example, the cold war, nuclear weaponry, nuclear test ban treaties, and antiballistic missiles.