  The energy splitting $E_{0a}$ in two and four dimensional Ising models is
measured in a cylindrical geometry on finite lattices. By comparing to exact
results in the two dimensional Ising model we demonstrate that $E_{0a}$ can be
extracted very reliably from Monte Carlo calculations in practice. In four
dimensions we compare the measured $E_{0a}$ with two different theoretical
predictions on the finite size behavior of the energy splitting. We find that
our numerical data are in favor of the predictions based on the semiclassical
dilute instanton gas approximation.
