Single-domain ferromagnetic cylinder

The so called fundamental theorem of W.F. Brown (1988) on spherical particles, which has recently been generalized to prolate spheroids, is extended to right circular finite cylinders. It is rigorously proved that for a cylinder with a radius R, the lowest free-energy state is that of uniform magnetization if R<R_c0, and an expression is given for the latter. For nonacicular cylinders, the result is rather close to that for an ellipsoid, but the difference between a cylinder and an ellipsoid is large when the cylinder is acicular