The Boltzmann probability distribution is defined by
Here E is the energy (or, more generally, the Hamiltonian) of the configuration, T is the temperature, and k is Boltzmann's constant. For convenience we often choose units so that k = 1, in which case T is measured in energy units.
Z is called the partition function, and is the fundamental quantity in statistical mechanics. All quantities of interest can be extracted from Z, so an analytic formula for Z implies an exact solution of the model. The sum will actually be an integral if the space of possible configurations is continuous rather than discrete.