Editing Canonical ensemble (section)

=== Ising model (strongly interacting system) ===

{{main|Ising model}}

In a system composed of pieces that interact with each other, it is usually not possible to find a way to separate the system into independent subsystems as done in the Boltzmann distribution. In these systems it is necessary to resort to using the full expression of the canonical ensemble in order to describe the thermodynamics of the system when it is thermostatted to a heat bath. The canonical ensemble is generally the most straightforward framework for studies of statistical mechanics and even allows one to obtain exact solutions in some interacting model systems.<ref>{{cite book | isbn = 9780120831807 | title = Exactly solved models in statistical mechanics | last1 = Baxter | first1 = Rodney J. | year = 1982 | publisher = Academic Press Inc.  }}</ref>

A classic example of this is the [[Ising model]], which is a widely discussed toy model for the phenomena of [[ferromagnetism]] and of [[self-assembled monolayer]] formation, and is one of the simplest models that shows a [[phase transition]]. [[Lars Onsager]] famously calculated exactly the free energy of an infinite-sized [[square-lattice Ising model]] at zero magnetic field, in the canonical ensemble.<ref>{{cite journal | last1 = Onsager | first1 = L. | title = Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition | doi = 10.1103/PhysRev.65.117 | journal = Physical Review | volume = 65 | issue = 3–4 | pages = 117–149 | year = 1944 |bibcode = 1944PhRv...65..117O }}</ref>