with C 0 being the cylinder sets defined above. Here, β = 1/ kT, where k is the Boltzmann constant, and T is the temperature. It is very common in mathematical treatments to set β = 1, as it is easily regained by rescaling the interaction energy. This partition function is written as a function of the interaction V to emphasize that it is only a function of the interaction, and not of any specific configuration of spins. The partition function, together with the Hamiltonian, are used to define a measure on the Borel σ-algebra in the following way: The measure of a cylinder set, i.e. an element of the base, is given by