Hi!
In the study of statistics, a given family of probability densities depending smoothly upon a parameter θ can be expressed in the form
p(x,θ)=exp[c(x)+∑rθrSr(x)−ψ(θ)],
where the variable x ranges over the sample space.
In models of statistical mechanics, we generally deal with Gibbs measures in the form
p(x,θ)=exp[∑rθrSr(x)−ln(ψ(θ))],
where the Sr determines the form of the action and ψ(θ)=lnZ(θ) is the partition function.
Based on the above, what is the meaning of x in Z?