Here the brackets, ⟨ ⟨ ⋅ ⋅ ⟩ ⟩ , indicate the above-mentioned thermal average. It is important to note here, however, that while the brackets are called an average, they are calculated as an expected value, not an average value. It is a matter of convention whether one subtracts the uncorrelated average product of s 1 and s 2 , ⟨ ⟨ s 1 ( R , t ) ⟩ ⟩ ⟨ ⟨ s 2 ( R + r , t + τ τ ) ⟩ ⟩ from the correlated product, ⟨ ⟨ s 1 ( R , t ) ⋅ ⋅ s 2 ( R + r , t + τ τ ) ⟩ ⟩ , with the convention differing among fields. The most common uses of correlation functions are when s 1 and s 2 describe the same variable, such as a spin-spin correlation function, or a particle position-position correlation function in an elemental liquid or a solid (often called a Radial distribution function or a pair correlation function). Correlation functions between the same random variable are autocorrelation functions. However, in statistical mechanics, not all correlation functions are autocorrelation functions. For example, in multicomponent condensed phases, the pair correlation function between different elements is often of interest. Such mixed-element pair correlation functions are an example of cross-correlation functions, as the random variables s 1 and s 2 represent the average variations in density as a function position for two distinct elements.