Percolation critical exponents

In the context of the physical and mathematical theory of percolation, a percolation transition is characterized by a set of universal critical exponents, which describe the fractal properties of the percolating medium at large scales and sufficiently close to the transition. The exponents are universal in the sense that they only depend on the type of percolation model and on the space dimension. They are expected to not depend on microscopic details such as the lattice structure, or whether site or bond percolation is considered. This article deals with the critical exponents of random percolation.

Percolating systems have a parameter ${\displaystyle p\,\!}$ which controls the occupancy of sites or bonds in the system. At a critical value ${\displaystyle p_{c}\,\!}$, the mean cluster size goes to infinity and the percolation transition takes place. As one approaches ${\displaystyle p_{c}\,\!}$, various quantities either diverge or go to a constant value by a power law in ${\displaystyle |p-p_{c}|\,\!}$, and the exponent of that power law is the critical exponent. While the exponent of that power law is generally the same on both sides of the threshold, the coefficient or "amplitude" is generally different, leading to a universal amplitude ratio.