the extraction of the isovector magnetic moment using twisted boundary conditions, we define the relative difference $$\label{eq:reldiff}
\d_L [F_2(B^2)] 
= 
\frac{\frac{2 M i }{B} \langle p(\bm{0}) \downarrow | J_3^+  | n(\bm{0}) \uparrow \rangle  -  F_2(B^2)}{F_2(B^2)}
.$$ In the limit $B \to 0$, the difference is just $\d_L [F_2(0)] = \d_L [\mu]$, the relative difference in the magnetic moment. In Fig. \[f:compare\], we plot $\d_L [\mu]$ as a function of $L$ for various values of the pion mass to contrast our results with those of Ref. [@Beane:2004tw].

![Comparison of finite volume effects for the isovector magnetic moment. Plotted versus $L$ is the relative difference $\d_L [\mu]$ for a few values of the pion mass. The total finite volume effect is denoted by $K + L$, while the contribution to $\d_L [\mu]$ from $\partial \cK_2 / \partial B$ alone is denoted by $K$. []{data-label="f:compare"}](compare.eps){width="55.00000%"}

We plot the total contribution to $\d_L[\mu]$ which arises from both the $\partial \cK_2 /\partial B$, and $\cL_{33}$ functions in Eq. , as well as just the contribution from $\partial \cK_2 /\partial B$. The latter is the dominant finite volume effect. Of course, to extract the magnetic moment, we require $\th \neq 0$ and thus we investigate $\d_L 