[F_2(B^2)]$ in Eq. . In Fig. \[f:theta\], we fix the lattice volume at $2.5 \, \texttt{fm}$ and plot the relative difference $\d_L [F_2(B^2)]$ as a function of $\th$ for a few values of the pion mass. We see that the effect of the finite volume decreases with $\th$. Generally the volume effects with momentum transfer (here the momentum transfer $q = B = \th / L$) are smaller than those at zero momentum transfer.[^8] In [@Detmold:2005pt] this was anticipated due to the loop pion mass appearing as $m_\pi^2 + x(1-x) q^2 > m_\pi^2$. There is also a simple physical interpretation for this effect: with a space-like momentum transfer the correlation function is being probed on distances of order $\sim 1/ \sqrt{q^2}$. As $q^2$ increases, the resolving power of the virtual probe diminishes the volume effect.

![Finite volume effects for extracting the isovector magnetic moment. Plotted versus $\th$ is the relative difference $\d_L [F_2(B^2)]$ for a few values of the pion mass. The momentum transfer from twisting is $B = \th \times 0.079   \, \texttt{GeV}$ []{data-label="f:theta"}](theta.eps){width="55.00000%"}

While twisted boundary conditions have introduced systematic error into the determination of the isovector moment, we stress that this is a controlled error. In a 