It is generally known that the orbital diamagnetism of a classical system of
charged particles in thermal equilibrium is identically zero -- the Bohr-van
Leeuwen theorem. Physically, this null result derives from the exact
cancellation of the orbital diamagnetic moment associated with the complete
cyclotron orbits of the charged particles by the paramagnetic moment subtended
by the incomplete orbits skipping the boundary in the opposite sense. Motivated
by this crucial, but subtle role of the boundary, we have simulated here the
case of a finite but \emph{unbounded} system, namely that of a charged particle
moving on the surface of a sphere in the presence of an externally applied
uniform magnetic field. Following a real space-time approach based on the
classical Langevin equation, we have computed the orbital magnetic moment which
now indeed turns out to be non-zero, and has the diamagnetic sign. To the best
of our knowledge, this is the first report of the possibility of finite
classical diamagnetism in principle, and it is due to the avoided cancellation.Comment: Accepted for publication in EP