Treffer: Finite Size Scaling

In this chapter we will introduce the theory of finite size scaling and demonstrate how we can apply the theory to improve our measurements of the properties of percolation clusters. Usually, we attempt to measure properties of percolation system in the largest possible system we can simulate. Here, we demonstrate that if the system behaves according to simple scaling relations, it is instead much better to systematically vary the system size and the interpolate to infinite system sizes. This approach is generally called finite size scaling and we provide a thorough introduction to the theory and its applications to understand the scaling of the density of the spanning cluster, $$P(p,L)$$ P ( p , L ) , the average cluster size, $$S(p,L)$$ S ( p , L ) , and the percolation probability $$\varPi (p,L)$$ Π ( p , L ) .