R. E. Peierls Pauli paramagnetism. Some further diamagnetism was due to the ion cores, but it seemed difficult to explain how the total susceptibility could become strongly negative, as in Bi. Clearly the assumption of free electrons was not good enough and one had to take the periodic potential of the lattice into account. How would one find the Landau diamagnetism for general Bloch states This seemed a hard problem because Landau's explanation appeared to depend on the discrete nature of the kinetic energy (at least in the plane perpendicular to the field ). One would thus have to find the actual eigenstates in the periodic potential and magnetic field. Moreover, collisions would broaden these levels by more than their spacing if the collision time was shorter than the Larmor period. It was a pleasant surprise (21) to discover that for statistical equilibrium the collision broadening and other effects were unimportant, as long as the energies associated with them were small compared to kr, even if they were larger than the level spacing. This made it possible to give a general expression for the Landau diamagnetism for any shape of the energy surface, except for inter-band terms, which were again hopefully regarded as later H. Jones put forward his model for Bi, which explained this fact, B ionand negligible. For Bi this implied a very sharp curvature of the energy function, and This led to speculation what would happen in strong magnetic fields at very low temperatures, and it became evident that one would get an oscillatory behaviour of the susceptibility, reminiscent of the mysterious effect discovered by de Haas and van Alphen Shoenberg has recently drawn my attention to the fact that this behaviour was already mentioned briefly in Landau s paper. Landau discounts the effect as unobservable. Evidently Landau had not heard of the de Haas-van Alphen experiments, and they never noticed the remark in his paper. Presumably I never read Landau's paper carefully, having had its main contents explained by him before publication, or, if I saw the remark, I accepted Landau's assurance that it was unobservable, and promptly forgot it To account for the experiments one had to make what seemed rather exotic assumptions about the shape of the Fermi surface and the occupation numbers in Bi, and even with that i did not manage to get a quantitative fit because I had not allowed for the possibility of several degenerate branches of the Fermi surface (23) Nevertheless i was convinced that the explanation was basically right. Numerical studies by Blackman later gave a better fit. 4) Then Landau showed how to obtain an approximate answer in closed form. (25) The relation of the de Haas-van Alphen oscillations with the geometry of the Fermi surface was later made transparent by My only other major contact with solid state problems in the pre-war days related to the connection between long-range order and the existence of a sharp phase transition, (27) My object was to stress the great qualitative difference between one and three dimensions. The argument also seemed to say that there could not be a sharp melting point in two dimensions, a result only recently upset by the work of Kosterlitz and thouless By the mid-1930s I had become interested in other problems and lost touch with36 R. E. Peierls Pauli paramagnetism. Some further diamagnetism was due to the ion cores, but it seemed difficult to explain how the total susceptibility could become strongly negative, as in Bi. Clearly the assumption of free electrons was not good enough, and one had to take the periodic potential of the lattice into account. How would one find the Landau diamagnetism for general Bloch states? This seemed a hard problem because Landau's explanation appeared to depend on the discrete nature of the kinetic energy (at least in the plane perpendicular to the field). One would thus have to find the actual eigenstates in the periodic potential and magnetic field. Moreover, collisions would broaden these levels by more than their spacing if the collision time was shorter than the Larmor period. It was a pleasant surprise(21) to discover that for statistical equilibrium the collision broadening and other effects were unimportant, as long as the energies associated with them were small compared to kT, even ifthey were larger than the level spacing. This made it possible to give a general. expression for the Landau diamagnetism for any shape of the energy surface, except for inter-band terms, which were again hopefully regarded as negligible. For Bi this implied a very sharp curvature of the energy function, and later H. Jones put forward his model for Bi, which explained this fact.(22) . This led to speculation what would happen in strong magnetic fields at very low temperatures, and it became evident that one would get an oscillatory behaviour of the susceptibility, reminiscent of the mysterious effect discovered by de Haas and van Alphen. Shoenberg has recently drawn my attention to the fact that this behaviour was already mentioned briefly in Landau's paper. Landau discounts the effect as unobservable. Evidently Landau had not heard of the de Haas-van Alphen experiments, and they never noticed the remark in his paper. Presumably I never read Landau's paper carefully, having had its main contents explained by him before publication, or, if I saw the remark, I accepted Landau's assurance that it was unobservable, and promptly forgot it. To account for the experiments one had to make what seemed rather exotic assumptions about the shape of the Fermi surface and the occupation numbers in Bi, and even with that I did not manage to get a quantitative fit because I had not allowed for the possibility of , several degenerate branches of the Fermi surface.(23) Nevertheless I was convinced that the explanation was basically right. Numerical studies by Blackman later gave a better fit.(24) Then Landau showed how to obtain an approximate answer in closed form.(25) The relation of the de Haas-van Alphen oscillations with the geometry of the Fermi surface was later made transparent by the beautiful argument of Onsager.(26) My only other major contact with solid state problems in the pre-war days related to the connection between long-range order and the existence of a sharp phase transition.(27) My object was to stress the great qualitative difference between one and three dimensions. The argument also seemed to say that there could not be a sharp melting point in two dimensions, a result only recently upset by the work of Kosterlitz and Thouless. By the mid-1930s I had become interested in other problems and lost touch with