Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: (1) Stirling’s approximation can be used to evaluate the number of microstates; ...

The Ising model for finite systems, e.g. for clusters of different sizes and crystal lattices, was solved analytically by the mean field approach. The magnetization was calculated from the number of accessible microstates, ...

solved in the microcanonical formalism because the number of accessible microstates can be easily evaluated. However, their solutions are usually presented using the Stirling approximation to deal with factorials. In this ...

The formation and stability of collisionless self-gravitating systems are long-standing problems, which date back to the work of D. Lynden-Bell on violent relaxation and extends to the issue of virialization of dark matter ...