Editing Statistical mechanics (section)

====Exact====
There are some cases which allow exact solutions.

* For very small microscopic systems, the ensembles can be directly computed by simply enumerating over all possible states of the system (using exact diagonalization in quantum mechanics, or integral over all phase space in classical mechanics).
* Some large systems consist of many separable microscopic systems, and each of the subsystems can be analysed independently. Notably, [[ideal gas|idealized gases]] of non-interacting particles have this property, allowing exact derivations of [[Maxwell–Boltzmann statistics]], [[Fermi–Dirac statistics]], and [[Bose–Einstein statistics]].<ref name="tolman"/>
* A few large systems with interaction have been solved. By the use of subtle mathematical techniques, exact solutions have been found for a few [[toy model]]s.<ref>{{cite book | isbn = 978-0-12-083180-7 | title = Exactly solved models in statistical mechanics | last1 = Baxter | first1 = Rodney J. | year = 1982 | publisher = Academic Press Inc. }}{{pn|date=April 2024}}</ref> Some examples include the [[Bethe ansatz]], [[square-lattice Ising model]] in zero field, [[hard hexagon model]].