  There has been much progress in the experimental measurement of the electric
and magnetic polarizabilities of the nucleon. Similarly, lattice QCD
simulations have recently produced dynamical QCD results for the magnetic
polarizability of the neutron approaching the chiral regime. In order to
compare the lattice simulations with experiment, calculation of partial
quenching and finite-volume effects is required prior to an extrapolation in
quark mass to the physical point. These dependencies are described using chiral
effective field theory. Corrections to the partial quenching effects associated
with the sea-quark-loop electric charges are estimated by modelling corrections
to the pion cloud. These are compared to the uncorrected lattice results. In
addition, the behaviour of the finite-volume corrections as a function of pion
mass is explored. Box sizes of approximately 7 fm are required to achieve a
result within 5% of the infinite-volume result at the physical pion mass. A
variety of extrapolations are shown at different box sizes, providing a
benchmark to guide future lattice QCD calculations of the magnetic
polarizabilities. A relatively precise value for the physical magnetic
polarizability of the neutron is presented, beta_n = 1.93(11)stat(8)sys x 10^-4
fm^3, which is in agreement with current experimental results.
