Often, one is interested in solely the spatial influence of a given random variable, say the direction of a spin, on its local environment, without considering later times, τ τ . In this case, we neglect the time evolution of the system, so the above definition is re-written with τ τ = 0 . This defines the equal-time correlation function, C ( r , 0 ) . It is written as: C ( r , 0 ) = ⟨ ⟨ s 1 ( R , t ) ⋅ ⋅ s 2 ( R + r , t ) ⟩ ⟩ − − ⟨ ⟨ s 1 ( R , t ) ⟩ ⟩ ⟨ ⟨ s 2 ( R + r , t ) ⟩ ⟩ .