  We study the two and four dimensional Nishimori multicritical point via high
temperature expansions for the $\pm J$ distribution, random-bond, Ising model.
In $2d$ we estimate the the critical exponents along the Nishimori line to be
$\gamma=2.37\pm 0.05$, $\nu=1.32\pm 0.08$. These, and earlier $3d$ estimates
$\gamma =1.80\pm 0.15$, $\nu=0.85\pm 0.08$ are remarkably close to the critical
exponents for percolation, which are known to be $\gamma=43/18$, $\nu=4/3$ in
$d=2$ and $\gamma=1.805\pm0.02$ and $\nu=0.875\pm 0.008$ in $d=3$. However, the
estimated $4d$ Nishimori exponents $\gamma=1.80\pm 0.15$, $\nu=1.0\pm 0.1$, are
quite distinct from the $4d$ percolation results $\gamma=1.435\pm 0.015$,
$\nu=0.678\pm 0.05$.
