I'm looking at two papers in particular: A. L. Efros and B. I. Shklovskii, Critical Behaviour of Conductivity and Dielectric Constant near the Metal-Non-Metal Transition Threshold, Phys. Status Solidi B 76, 475 (1976) and Measurement of the conductivity exponent in random percolating networks of nanoscale bismuth clusters .
In percolation theory, for concentrations $p$ higher than the critical concentration $p_c$, the conductivity $\sigma \propto (p-p_c)^t$ for $p>p_c$, where $t$ is 1.3 for 2 dimensions. It's often simplified so that the substrate is a perfect insulator, so you have $\sigma=0$ for $p<p_c$. So it should look pretty simple, something like:
My point is, concave up. However, looking at the two papers I mentioned above, they have these graphs:
with:
and:
Both of which are concave down in the region $p>p_c$.
Is there something going on, or is this a series of errors?
I suspect the Efros paper may have just had an error, as the caption corresponding to the dotted line (1) points to the region of $x<x_c$, where they explicitly said that equation doesn't apply. It does have a very strange scale though.
I have no idea what's going on in the graph of the second paper. Is there any explanation besides an error?
Thank you!