Tunneling and energy splitting in Ising models

Abstract

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.