I am having a little difficulty with a calculation in "The connective constant of the honeycomb lattice equals $\sqrt{2+\sqrt2}$", Hugo Duminil-Copin, Stanislav Smirnov, (arXiv:1007.0575).
On page 4 of the paper, in the second equation block, it is shown that $c( \gamma_1) + c(\gamma_ 2) = 0$.
Would someone be able to fill out the details of this calculation?
In particular where does $j$ come from and how does the $(p-v)$ factor get there. I can sort of see how it works and how it uses the equation block above but I am left with extra factors. I can also 'reverse engineer' j to determine its value. Is it perhaps just a placeholder and the authors haven't made this clear? I know that sometimes $j$ is used instead of $i$ but I don't think it is being used like this.
Many thanks
Mark