Disclaimer: I am just learning about percolation theory for the first time, so I am not too familiar with some of the terminology.
Suppose you have a 2-D square lattice with bonds connecting sites. The probability that a bond is "open" is given by $p$ and the corresponding probability that a bond is "closed" is given by $1-p$. For an infinite lattice, there exists the critical threshold $p_c$ where a single cluster of open bonds will form an infinite cluster. Additionally, there is some probability $P(p)$ that any given bond will belong to this infinite cluster.
When $p < p_c$, then $P(p) = 0$ since no infinite cluster exists. However, when $p\geq p_c$, then
$$P(p)\approx A(p-p_c)^\beta .$$
Most of the above info comes from pg 196 of Clerc et al., 1990, The electrical conductivity of binary disordered systems, percolation clusters, fractals and related models.
The issue is, Clerc et al. never define $A$ or $\beta$!
Looking on Wikipedia, I believe the critical exponent I'm looking for is called the "backbone" critical exponent and has a value of $\beta = 1.64$ (denoted $d_B$ in the Wikipedia article).
However, I am not sure what the value of $A$ is. I have looked in many places and many authors simply say that $P(p)$ is proportional to $(p-p_c)^\beta$ without ever defining what the scaling factor is.
My question: What is the value of $A$ for a 2-D square network of bonds and sites as defined above?
Any help is appreciated.