correlation functions (8.11 )

The correlation function shows the relationship between a specific a spin S0 and its neighbors Si the function can be described as :

 The program cycles through each spin in a 20 x 20 lattice. for each spin at a given point S0, the average values of its neighbors Si are multiplied together. To start Si is = 1 so the neighbors are the immediate spins nearest to s0. This goes through all the way to i = 10/ The results of which can be seen below for varying temperatures. 

Figure 1 - Correlation Function simulated

Figure 2 - Correlation Function from Computational Physics by Giordano (Fig 8.11) [1]